Finite Group Databasebeta

← Group #13156751

Character table — Group #13156751

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444488888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12222222333666666666666666666666333666666666666666666666366666664444441212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212122222444444446666121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ911-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11-11-1i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−ii−i
χ1011-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11-11-1−ii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−ii
χ1111-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11-1-11i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i−i−iii-1-111ii−i−i−i−iii−ii
χ1211-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11-1-11−ii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111−i−iiiii−i−i-1-111−i−iiiii−i−ii−i
χ1311-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-111-1i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-111−i−iiiii−i−i-1-111−i−iiiii−i−i−ii
χ1411-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-111-1−ii-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i−i−iii-1-111ii−i−i−i−iiii−i
χ1511-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-11-11i−i-1-1-1-11111-1-1-1-11111iiii−i−i−i−i-1-1-1-11111-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii−i−iii11-1-1−i−iii−i−iiii−i
χ1611-1-111-1-11111111-1-1-1-11-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-11-11−ii-1-1-1-11111-1-1-1-11111−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i−ii
χ172222222222-122222222-1-1-1-1-12222-1-1222-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-122220022-1-122-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000222200000000-1-1-1-10000000000
χ182222222222-122222222-1-1-1-1-12222-1-1222-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-122-2-20022-1-122-1-1-2-211-2-21100000000-1-1-1-1-1-1-1-11111111100000000-2-2-2-20000000011110000000000
χ192222222222-122222222-1-1-1-1-12222-1-1222-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-22200-2-211-2-21122-1-122-1-10000000011111111-1-1-1-1-1-1-1-100000000-2-2-2-20000000011110000000000
χ202222222222-122222222-1-1-1-1-12222-1-1222-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-200-2-211-2-211-2-211-2-21100000000111111111111111100000000222200000000-1-1-1-10000000000
χ21222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-1-1-100222200000000-1-122-1-12222-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000222200000000-1-1-1-100
χ22222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-1-1-10022-2-200000000-1-122-1-122-2-211-2-21100000000-1-1-1-1-1-1-1-11111111100000000-2-2-2-200000000111100
χ23222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-1-1-100-2-2220000000011-2-211-2-222-1-122-1-10000000011111111-1-1-1-1-1-1-1-100000000-2-2-2-200000000111100
χ24222222222-1222-1-122-1-1222222-12-1222-1-12-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000011-2-211-2-2-2-211-2-21100000000111111111111111100000000222200000000-1-1-1-100
χ2522222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-12222-12-1-1-1-1-1-1-1-1-1220022-1-122-1-12200000000-1-122-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000222200000000-1-1-1-1000000
χ2622222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-12222-12-1-1-1-1-1-1-1-1-12200-2-2-1-122-1-1220000000011-2-211-2-2-1-1-1-1-1-1-1-100000000111111110000-2-2-2-2000000001111000000
χ2722222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-12222-12-1-1-1-1-1-1-1-1-1-2-2002211-2-211-2-200000000-1-122-1-1221111111100000000-1-1-1-1-1-1-1-10000-2-2-2-2000000001111000000
χ2822222222-122-1-122-1-12222222-12-1222-12-1-12-1-1-1-1-122-1-1-1-1-1-1-12222-12-1-1-1-1-1-1-1-1-1-2-200-2-211-2-211-2-20000000011-2-211-2-21111111100000000111111110000222200000000-1-1-1-1000000
χ292222-2-2-2-22222-22-22222222-2-2-2-2-2-2-2-2-2-22222-2-22-22-222-222-2-222-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000000000000002-22-2000000002-22-20000000000
χ302222-2-2-2-22222-22-22222222-2-2-2-2-2-2-2-2-2-22222-2-22-22-222-222-2-222-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000000000-22-2200000000-22-220000000000
χ312222-2-2-2-222-12-22-22222-1-1-111-2-2-2-211-2-22-1-12-2-2-11-1122-2-1-111-1-11111-2-1-111-1-111000000003−3003−3003−3003−30000000033−3−333−3−333−3−333−3−3000000002-22-200000000-11-110000000000
χ322222-2-2-2-222-12-22-22222-1-1-111-2-2-2-211-2-22-1-12-2-2-11-1122-2-1-111-1-11111-2-1-111-1-111000000003−3003−300−3300−330000000033−3−333−3−3−3−333−3−33300000000-22-22000000001-11-10000000000
χ332222-2-2-2-222-12-22-22222-1-1-111-2-2-2-211-2-22-1-12-2-2-11-1122-2-1-111-1-11111-2-1-111-1-11100000000−3300−33003−3003−300000000−3−333−3−33333−3−333−3−300000000-22-22000000001-11-10000000000
χ342222-2-2-2-222-12-22-22222-1-1-111-2-2-2-211-2-22-1-12-2-2-11-1122-2-1-111-1-11111-2-1-111-1-11100000000−3300−3300−3300−3300000000−3−333−3−333−3−333−3−333000000002-22-200000000-11-110000000000
χ3522-2-222-2-222-12222-2-2-2-2-1111122-2-2-1-1-2-22-1-1222-1-1-1-1-2-2-211111111-1-1-2-1-1-1-111112-22-20022-1-1-2-21122-1-1-2-21100000000-1-1-1-11111-1-1-1-111110000000022-2-200000000-1-1110000000000
χ3622-2-222-2-222-12222-2-2-2-2-1111122-2-2-1-1-2-22-1-1222-1-1-1-1-2-2-211111111-1-1-2-1-1-1-111112-2-220022-1-1-2-211-2-21122-1-100000000-1-1-1-111111111-1-1-1-100000000-2-2220000000011-1-10000000000
χ3722-2-222-2-222-12222-2-2-2-2-1111122-2-2-1-1-2-22-1-1222-1-1-1-1-2-2-211111111-1-1-2-1-1-1-11111-222-200-2-21122-1-122-1-1-2-211000000001111-1-1-1-1-1-1-1-1111100000000-2-2220000000011-1-10000000000
χ3822-2-222-2-222-12222-2-2-2-2-1111122-2-2-1-1-2-22-1-1222-1-1-1-1-2-2-211111111-1-1-2-1-1-1-11111-22-2200-2-21122-1-1-2-21122-1-1000000001111-1-1-1-11111-1-1-1-10000000022-2-200000000-1-1110000000000
χ3922-2-222-2-22-1222-1-1-2-2112-2-2-2-22-1-2122-21-12-1-1-1-122-1-1111-2-2-2-211112-11-1-1-1-11111002-22i−2i00000000-1-12211-2-22i2i−i−i−2i−2iii00000000-1-1-1-11111−i−i−i−iiiii000000002i2i−2i−2i00000000−i−iii00
χ4022-2-222-2-22-1222-1-1-2-2112-2-2-2-22-1-2122-21-12-1-1-1-122-1-1111-2-2-2-211112-11-1-1-1-11111002-2−2i2i00000000-1-12211-2-2−2i−2iii2i2i−i−i00000000-1-1-1-11111iiii−i−i−i−i00000000−2i−2i2i2i00000000ii−i−i00
χ4122-2-222-2-22-1222-1-1-2-2112-2-2-2-22-1-2122-21-12-1-1-1-122-1-1111-2-2-2-211112-11-1-1-1-1111100-222i−2i0000000011-2-2-1-1222i2i−i−i−2i−2iii000000001111-1-1-1-1−i−i−i−iiiii00000000−2i−2i2i2i00000000ii−i−i00
χ4222-2-222-2-22-1222-1-1-2-2112-2-2-2-22-1-2122-21-12-1-1-1-122-1-1111-2-2-2-211112-11-1-1-1-1111100-22−2i2i0000000011-2-2-1-122−2i−2iii2i2i−i−i000000001111-1-1-1-1iiii−i−i−i−i000000002i2i−2i−2i00000000−i−iii00
χ4322-2-222-2-2-122-1-12211-2-22-2-2-2-2-121-2221-2-1-12-1-1-1-1-1221111111-2-2-2-2-121-1-1-1-111112-2002i−2i-1-12211-2-200000000−i−i2i2iii−2i−2i-1-1-1-1111100000000−i−i−i−iiiii00002i2i−2i−2i00000000−i−iii000000
χ4422-2-222-2-2-122-1-12211-2-22-2-2-2-2-121-2221-2-1-12-1-1-1-1-1221111111-2-2-2-2-121-1-1-1-111112-200−2i2i-1-12211-2-200000000ii−2i−2i−i−i2i2i-1-1-1-1111100000000iiii−i−i−i−i0000−2i−2i2i2i00000000ii−i−i000000
χ4522-2-222-2-2-122-1-12211-2-22-2-2-2-2-121-2221-2-1-12-1-1-1-1-1221111111-2-2-2-2-121-1-1-1-11111-22002i−2i11-2-2-1-12200000000−i−i2i2iii−2i−2i1111-1-1-1-100000000−i−i−i−iiiii0000−2i−2i2i2i00000000ii−i−i000000
χ4622-2-222-2-2-122-1-12211-2-22-2-2-2-2-121-2221-2-1-12-1-1-1-1-1221111111-2-2-2-2-121-1-1-1-11111-2200−2i2i11-2-2-1-12200000000ii−2i−2i−i−i2i2i1111-1-1-1-100000000iiii−i−i−i−i00002i2i−2i−2i00000000−i−iii000000
χ4722-2-2-2-2222222-22-2-2-2-2-22-2-222-2-222-2-2222222-2-22-22-2-2-22-2-222-2-222-2-2222-2-2-2-2220000000000000000000000000000000000000000000000000000002-2-22000000002-2-220000000000
χ4822-2-2-2-2222222-22-2-2-2-2-22-2-222-2-222-2-2222222-2-22-22-2-2-22-2-222-2-222-2-2222-2-2-2-222000000000000000000000000000000000000000000000000000000-222-200000000-222-20000000000
χ4922-2-2-2-22222-12-22-2-2-2-2-2-111-1-1-2-22211222-1-12-2-2-11-11-2-2211-1-111-1-1112-1-11111-1-1000000003−300−33003−300−330000000033−3−3−3−33333−3−3−3−333000000002-2-2200000000-111-10000000000
χ5022-2-2-2-22222-12-22-2-2-2-2-2-111-1-1-2-22211222-1-12-2-2-11-11-2-2211-1-111-1-1112-1-11111-1-1000000003−300−3300−33003−30000000033−3−3−3−333−3−33333−3−300000000-222-2000000001-1-110000000000
χ5122-2-2-2-22222-12-22-2-2-2-2-2-111-1-1-2-22211222-1-12-2-2-11-11-2-2211-1-111-1-1112-1-11111-1-100000000−33003−3003−300−3300000000−3−33333−3−333−3−3−3−33300000000-222-2000000001-1-110000000000
χ5222-2-2-2-22222-12-22-2-2-2-2-2-111-1-1-2-22211222-1-12-2-2-11-11-2-2211-1-111-1-1112-1-11111-1-100000000−33003−300−33003−300000000−3−33333−3−3−3−33333−3−3000000002-2-2200000000-111-10000000000
χ532-22-22-22-2222-22-2-22-22-2-22-22-2-22222-2-2-2222-22-2-22-2-22-2-22-22-22-22-2-2222-22-22-22-200000000000000000000000000000000000000000000000000000000002i−2i2i−2i000000002i−2i2i−2i000000
χ542-22-22-22-2222-22-2-22-22-2-22-22-2-22222-2-2-2222-22-2-22-2-22-2-22-22-22-22-2-2222-22-22-22-20000000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000−2i2i−2i2i000000
χ552-22-22-22-2-1221-1-2-2-112-2-22-22-212-122-21-2-1-121-111-1-2-2-111-11-112-22-212-1-11-11-11-110000003−3003−30000000000−i3i300−i3i3003−33−33−33−300000000−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i00000000−ii−ii000000
χ562-22-22-22-2-1221-1-2-2-112-2-22-22-212-122-21-2-1-121-111-1-2-2-111-11-112-22-212-1-11-11-11-110000003−3003−30000000000i3−i300i3−i3003−33−33−33−300000000i3i3−i3−i3i3i3−i3−i30000−2i2i−2i2i00000000i−ii−i000000
χ572-22-22-22-2-1221-1-2-2-112-2-22-22-212-122-21-2-1-121-111-1-2-2-111-11-112-22-212-1-11-11-11-11000000−3300−330000000000−i3i300−i3i300−33−33−33−3300000000−i3−i3i3i3−i3−i3i3i30000−2i2i−2i2i00000000i−ii−i000000
χ582-22-22-22-2-1221-1-2-2-112-2-22-22-212-122-21-2-1-121-111-1-2-2-111-11-112-22-212-1-11-11-11-11000000−3300−330000000000i3−i300i3−i300−33−33−33−3300000000i3i3−i3−i3i3i3−i3−i300002i−2i2i−2i00000000−ii−ii000000
χ592-22-2-22-22222-2-2-222-22-2-22-2-222-2-2-2-2222222-2-22-2-2-222-222-2-222-2-222-2-22-2-222-2-22000000000000000000000000000000000000000000000000000000000000002-22-2000000002-22-200
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χ1074-44-44-44-44-2-2-44224-4-222-22-22-4-24-2-22-42-2-212-222-2-1-1-222-22-221-11-121-21-11-11-11-1000000000000000000000000000000000000003-3-333-3-330000000000000000000000000000000000
χ1084-44-44-44-44-2-2-44224-4-222-22-22-4-24-2-22-42-2-212-222-2-1-1-222-22-221-11-121-21-11-11-11-100000000000000000000000000000000000000-333-3-333-30000000000000000000000000000000000
χ1094-44-44-44-4-24-22-2-4-4-224-42-22-2224-24-222-4-21-22-22-1122-2221-11-1-22-22-1-2-21-11-11-11-100000023−230023−23000000000000000000−33−33−33−33000000000000000000000000000000000000000000
χ1104-44-44-44-4-24-22-2-4-4-224-42-22-2224-24-222-4-21-22-22-1122-2221-11-1-22-22-1-2-21-11-11-11-1000000−232300−23230000000000000000003−33−33−33−3000000000000000000000000000000000000000000
χ1114-44-44-44-4-2-242-222-22-22-44-44-42-2-2-24-4221-2-2-11-12-2221-1-1-22-22-22-222-211-11-11-11-10000000000000000000000−2i32i300−2i32i3000000000000000000i3i3−i3−i3i3i3−i3−i300000000000000000000000000
χ1124-44-44-44-4-2-242-222-22-22-44-44-42-2-2-24-4221-2-2-11-12-2221-1-1-22-22-22-222-211-11-11-11-100000000000000000000002i3−2i3002i3−2i3000000000000000000−i3−i3i3i3−i3−i3i3i300000000000000000000000000
χ1134-44-4-44-4444-2-4-4-444-44-42-222-24-4-4-42-2444-2-2-4-44222-24-44-222-2-222-2-22-4-222-2-222-200000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-44-4-44-444-2-2-4-42-24-4-222-222-242-422-24-2-2-2122-222-11-22-2-222-21-1-11-2-121-1-111-1-110000000000000023−230023−23000000000000000000−33−33−33−330000000000000000000000000000000000
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χ1418-88-88-88-8-4-4-44-444-44-444-44-444-4-4-4-4444222-22-2-22-2-22-2-22-22-22-22-2-222-11-11-11-1100000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-8-88-88-4-4-4444-4-44-444-444-4-44444-4-4-4222-2-22-2-2-222-222-2-222-2-222-2-2-111-1-111-100000000000000000000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).