Finite Group Databasebeta

← Group #11787636

Character table — Group #11787636

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444444444444888888888888888812121212121212121212121212121212121212121212121212121212121212121212121224242424242472727272
order1244222334446666121212121212366666666888812121212121212121224242424242424246612122424242424242424242424242244666688888888121212122424242424242424242424242424242488242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ911-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11ii−i−i111-111-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1i−i
χ1011-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11ii−i−i111-111-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i1-11-111-1-1ii−i−i−i−iii11-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11−ii
χ1111-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11ii−i−i111-111-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i-11-11-1-111−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-11−ii
χ1211-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11ii−i−i111-111-1-1-1iiii−i−i−i−i1-11-1ii−i−iiiii−i−i−i−i-11-11-1-111−i−iii−i−iii-1-111−i−i−i−iiiii−i−i−i−iiiii-11-1-1111-1i−i
χ1311-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11−i−iii111-111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii1-11-111-1-1−i−iiiii−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11i−i
χ1411-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11−i−iii111-111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1−ii
χ1511-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11−i−iii111-111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i-1-111iiii−i−i−i−iiiii−i−i−i−i-11-1-1111-1−ii
χ1611-1-11-1-11111-1-1-111-1-111-1-111-11-1-1-1-11−i−iii111-111-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−i−i−iiiii-11-11-1-111ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1-11i−i
χ1722222222-1222222-12222-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ1822222222-1222222-12222-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-20000111111111111000000000000000000
χ1922222222-1222222-12222-1-1-122-1-1-1-1-1-1-2-2-2-22-1-1-1-1-1-1-1211111111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-2-2-20000-1-1-1-111111111000000000000000000
χ2022222222-1222222-12222-1-1-122-1-1-1-1-1-1-2-2-2-22-1-1-1-1-1-1-1211111111-1-1-1-1-2-2-2-211111111-2-2-2-21111222200001111-1-1-1-1-1-1-1-1000000000000000000
χ212222222-12222-1-1-12-1-1-1-122-1-1-1222-1-1-12222-1222-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-122-1-1-1-10000
χ222222222-12222-1-1-12-1-1-1-122-1-1-1222-1-1-12222-1222-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111-2-211110000
χ232222222-12222-1-1-12-1-1-1-122-1-1-1222-1-1-1-2-2-2-2-1222-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111110000000000002222000000000000-1-1-1-1-1-1-1-1-2-211110000
χ242222222-12222-1-1-12-1-1-1-122-1-1-1222-1-1-1-2-2-2-2-1222-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111000000000000-2-2-2-20000000000001111111122-1-1-1-10000
χ2522222-2-222-2-22-2-22222-2-22222-22-2-2-2-220000-2-2-22-2-2222000000002-2-22000000000000000000002-22-20000000022-2-222-2-2000000000000000000
χ2622222-2-222-2-22-2-22222-2-22222-22-2-2-2-220000-2-2-22-2-2222000000002-2-2200000000000000000000-22-2200000000-2-222-2-222000000000000000000
χ2722222-2-22-1-2-22-2-22-122-2-2-1-1-12-2-11111-10000-211-111-1-12−i3−i3i3i3−i3−i3i3i3-111-10000−i3−i3i3i3−i3−i3i3i30000−i3i3−i3i32-22-20000−i3i3−i3i3-1-111-1-111000000000000000000
χ2822222-2-22-1-2-22-2-22-122-2-2-1-1-12-2-11111-10000-211-111-1-12−i3−i3i3i3−i3−i3i3i3-111-10000−i3−i3i3i3−i3−i3i3i30000i3−i3i3−i3-22-220000i3−i3i3−i311-1-111-1-1000000000000000000
χ2922222-2-22-1-2-22-2-22-122-2-2-1-1-12-2-11111-10000-211-111-1-12i3i3−i3−i3i3i3−i3−i3-111-10000i3i3−i3−i3i3i3−i3−i30000−i3i3−i3i3-22-220000−i3i3−i3i311-1-111-1-1000000000000000000
χ3022222-2-22-1-2-22-2-22-122-2-2-1-1-12-2-11111-10000-211-111-1-12i3i3−i3−i3i3i3−i3−i3-111-10000i3i3−i3−i3i3i3−i3−i30000i3−i3i3−i32-22-20000i3−i3i3−i3-1-111-1-111000000000000000000
χ312222-22-222-22-222222222222-2-2-22-22220000-22-2-22222-200000000-2-2-2-20000000000002-2-2222-2-200000000-2-22200000000000000000000000000
χ322222-22-222-22-222222222222-2-2-22-22220000-22-2-22222-200000000-2-2-2-2000000000000-222-2-2-2220000000022-2-200000000000000000000000000
χ332222-22-22-1-22-2222-12222-1-1-1-2-21-11-1-1-10000-2-111-1-1-1-1-2−i3i3−i3i3−i3i3−i3i311110000−i3i3−i3i3−i3i3−i3i32-2-22-1-1110000000011-1-1−i3i3−i3i3−i3i3−i3i3000000000000000000
χ342222-22-22-1-22-2222-12222-1-1-1-2-21-11-1-1-10000-2-111-1-1-1-1-2−i3i3−i3i3−i3i3−i3i311110000−i3i3−i3i3−i3i3−i3i3-222-211-1-100000000-1-111i3−i3i3−i3i3−i3i3−i3000000000000000000
χ352222-22-22-1-22-2222-12222-1-1-1-2-21-11-1-1-10000-2-111-1-1-1-1-2i3−i3i3−i3i3−i3i3−i311110000i3−i3i3−i3i3−i3i3−i32-2-22-1-1110000000011-1-1i3−i3i3−i3i3−i3i3−i3000000000000000000
χ362222-22-22-1-22-2222-12222-1-1-1-2-21-11-1-1-10000-2-111-1-1-1-1-2i3−i3i3−i3i3−i3i3−i311110000i3−i3i3−i3i3−i3i3−i3-222-211-1-100000000-1-111−i3i3−i3i3−i3i3−i3i3000000000000000000
χ372222-2-22222-2-2-2-22222-2-2222-22-2-22-2-222-22-22-22-2-2-222-22-2-222-2-22-222-22-22-22-2-222-2-220000000000000000000000000000000000000000000000
χ382222-2-22222-2-2-2-22222-2-2222-22-2-22-2-22-22-222-22-2-2-222-2-222-2-222-2-222-2-22-22-222-2-222-20000000000000000000000000000000000000000000000
χ392222-2-222-12-2-2-2-22-122-2-2-1-1-1-2211-111-12-22-221-1111-1-1-2-111-1-111-11-1-112-22-2-111-1-111-10000−i3i3i3−i300000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ402222-2-222-12-2-2-2-22-122-2-2-1-1-1-2211-111-12-22-221-1111-1-1-2-111-1-111-11-1-112-22-2-111-1-111-10000i3−i3−i3i300000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ412222-2-222-12-2-2-2-22-122-2-2-1-1-1-2211-111-1-22-2221-1111-1-1-21-1-111-1-111-1-11-22-221-1-111-1-110000−i3i3i3−i300000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ422222-2-222-12-2-2-2-22-122-2-2-1-1-1-2211-111-1-22-2221-1111-1-1-21-1-111-1-111-1-11-22-221-1-111-1-110000i3−i3−i3i300000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ432222-2-22-122-2-211-12-1-11122-11-1-2-2211-12-22-2-1-22-211-1-112-2-222-2-221-1-11-11-11-111-1-111-1000000000000000000000000000033−3−333−3−3003−33−30000
χ442222-2-22-122-2-211-12-1-11122-11-1-2-2211-12-22-2-1-22-211-1-112-2-222-2-221-1-11-11-11-111-1-111-10000000000000000000000000000−3−333−3−33300−33−330000
χ452222-2-22-122-2-211-12-1-11122-11-1-2-2211-1-22-22-1-22-211-1-11-222-2-222-21-1-111-11-11-1-111-1-11000000000000000000000000000033−3−333−3−300−33−330000
χ462222-2-22-122-2-211-12-1-11122-11-1-2-2211-1-22-22-1-22-211-1-11-222-2-222-21-1-111-11-11-1-111-1-110000000000000000000000000000−3−333−3−333003−33−30000
χ4722-2-222222-2-2-22222-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-2000000000000000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ4822-2-222222-2-2-22222-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2-20000000022-2-200000000000000000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ4922-2-22222-1-2-2-2222-1-2-2-2-211-122-1-1-1-1-1-10000-21111111-233−3−3−3−333-1-111000033−3−3−3−3330000−i3i3i3−i32i−2i−2i2i0000−i3i3i3−i3−i−iiiii−i−i000000000000000000
χ5022-2-22222-1-2-2-2222-1-2-2-2-211-122-1-1-1-1-1-10000-21111111-233−3−3−3−333-1-111000033−3−3−3−3330000i3−i3−i3i3−2i2i2i−2i0000i3−i3−i3i3ii−i−i−i−iii000000000000000000
χ5122-2-22222-1-2-2-2222-1-2-2-2-211-122-1-1-1-1-1-10000-21111111-2−3−33333−3−3-1-1110000−3−33333−3−30000−i3i3i3−i3−2i2i2i−2i0000−i3i3i3−i3ii−i−i−i−iii000000000000000000
χ5222-2-22222-1-2-2-2222-1-2-2-2-211-122-1-1-1-1-1-10000-21111111-2−3−33333−3−3-1-1110000−3−33333−3−30000i3−i3−i3i32i−2i−2i2i0000i3−i3−i3i3−i−iiiii−i−i000000000000000000
χ5322-2-22-2-22-122-2-2-22-1-2-22211-12-2-11111-12i2i−2i−2i2-1-11-1-111-2−i−i−i−iiiii-11-112i2i−2i−2i−i−i−i−iiiii2-22-2-1-1112i2i−2i−2i0000-1-111−i−i−i−iiiii000000000000000000
χ5422-2-22-2-22-122-2-2-22-1-2-22211-12-2-11111-12i2i−2i−2i2-1-11-1-111-2−i−i−i−iiiii-11-112i2i−2i−2i−i−i−i−iiiii-22-2211-1-1−2i−2i2i2i000011-1-1iiii−i−i−i−i000000000000000000
χ5522-2-22-2-22-122-2-2-22-1-2-22211-12-2-11111-1−2i−2i2i2i2-1-11-1-111-2iiii−i−i−i−i-11-11−2i−2i2i2iiiii−i−i−i−i2-22-2-1-111−2i−2i2i2i0000-1-111iiii−i−i−i−i000000000000000000
χ5622-2-22-2-22-122-2-2-22-1-2-22211-12-2-11111-1−2i−2i2i2i2-1-11-1-111-2iiii−i−i−i−i-11-11−2i−2i2i2iiiii−i−i−i−i-22-2211-1-12i2i−2i−2i000011-1-1−i−i−i−iiiii000000000000000000
χ5722-2-22-2-2-1222-211-1211-1-1-2-2-1-112-2-211-12i2i−2i−2i-122-2-1-11112i2i2i2i−2i−2i−2i−2i-11-11−i−iii−i−i−i−iiiii0000000000002i2i−2i−2i000000000000−i−i−i−iiiii2-2-1-1110000
χ5822-2-22-2-2-1222-211-1211-1-1-2-2-1-112-2-211-12i2i−2i−2i-122-2-1-11112i2i2i2i−2i−2i−2i−2i-11-11−i−iii−i−i−i−iiiii000000000000−2i−2i2i2i000000000000iiii−i−i−i−i-2211-1-10000
χ5922-2-22-2-2-1222-211-1211-1-1-2-2-1-112-2-211-1−2i−2i2i2i-122-2-1-1111−2i−2i−2i−2i2i2i2i2i-11-11ii−i−iiiii−i−i−i−i0000000000002i2i−2i−2i000000000000−i−i−i−iiiii-2211-1-10000
χ6022-2-22-2-2-1222-211-1211-1-1-2-2-1-112-2-211-1−2i−2i2i2i-122-2-1-1111−2i−2i−2i−2i2i2i2i2i-11-11ii−i−iiiii−i−i−i−i000000000000−2i−2i2i2i000000000000iiii−i−i−i−i2-2-1-1110000
χ6122-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22-22222i−2i−2i2i2-222-2-2-2-222i−2i−2i2i−2i2i2i−2i-2-2222i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000
χ6222-2-2-22-2222-222222-2-2-2-2-2-22-2-2-22-2222−2i2i2i−2i2-222-2-2-2-22−2i2i2i−2i2i−2i−2i2i-2-222−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000
χ6322-2-2-22-22-12-22222-1-2-2-2-211-1-2-21-11-1-1-12i−2i−2i2i21-1-111112−iii−ii−i−ii11-1-12i−2i−2i2i−iii−ii−i−ii0000−i3i3−i3i300000000i3−i3i3−i33−3−33−333−3000000000000000000
χ6422-2-2-22-22-12-22222-1-2-2-2-211-1-2-21-11-1-1-12i−2i−2i2i21-1-111112−iii−ii−i−ii11-1-12i−2i−2i2i−iii−ii−i−ii0000i3−i3i3−i300000000−i3i3−i3i3−333−33−3−33000000000000000000
χ6522-2-2-22-22-12-22222-1-2-2-2-211-1-2-21-11-1-1-1−2i2i2i−2i21-1-111112i−i−ii−iii−i11-1-1−2i2i2i−2ii−i−ii−iii−i0000−i3i3−i3i300000000i3−i3i3−i3−333−33−3−33000000000000000000
χ6622-2-2-22-22-12-22222-1-2-2-2-211-1-2-21-11-1-1-1−2i2i2i−2i21-1-111112i−i−ii−iii−i11-1-1−2i2i2i−2ii−i−ii−iii−i0000i3−i3i3−i300000000−i3i3−i3i33−3−33−333−3000000000000000000
χ6722-2-2-22-2-122-22-1-1-121111-2-2-111-22-2-1-1-12i−2i−2i2i-1-2221111-12i−2i−2i2i−2i2i2i−2i11-1-1−iii−i−iii−ii−i−ii0000000000000000000000000000−i3−i3i3i3i3i3−i3−i300−333−30000
χ6822-2-2-22-2-122-22-1-1-121111-2-2-111-22-2-1-1-12i−2i−2i2i-1-2221111-12i−2i−2i2i−2i2i2i−2i11-1-1−iii−i−iii−ii−i−ii0000000000000000000000000000i3i3−i3−i3−i3−i3i3i3003−3−330000
χ6922-2-2-22-2-122-22-1-1-121111-2-2-111-22-2-1-1-1−2i2i2i−2i-1-2221111-1−2i2i2i−2i2i−2i−2i2i11-1-1i−i−iii−i−ii−iii−i0000000000000000000000000000−i3−i3i3i3i3i3−i3−i3003−3−330000
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χ7122-2-2-2-2222-222-2-222-2-222-2-22-22-2-22-2-220000-22-2222-2-2200000000-22-2200000000000022-2-2222200000000-2-2-2-200000000000000000000000000
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χ1054-4−4i4i000-24000−2i32i32-42i−2i−2323−4i4i-200000−2i32i3200000000−23232i−2i0000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ230000000000
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χ1098-88i−8i0008-400000-848i−8i00−4i4i-4000000040000000000−4i4i00000000000000000000000000000000000000000000000000000000000000000000000
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χ1118-88i−8i000-4-40004i3−4i344−4i4i−4343−4i4i200000−2i32i3-20000000023−232i−2i00000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8−8i8i0008-400000-84−8i8i004i−4i-40000000400000000004i−4i00000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8−8i8i000-4-4000−4i34i3444i−4i−43434i−4i2000002i3−2i3-20000000023−23−2i2i00000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8−8i8i000-4-40004i3−4i3444i−4i43−434i−4i200000−2i32i3-200000000−2323−2i2i00000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.