Finite Group Databasebeta

← Group #13155647

Character table — Group #13155647

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order12223334466666666633366666666612121212121212121212888836661212121212121212444444441212121212121212242424242424242424242424242424244412121212121212121212121212121212224412128888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111
χ911-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1ii−i−i1-1-111-11-111-1-1ii−i−i1-1i−i11-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−iii−i−ii−i1-1ii−i−i11-1-11-1i−ii−i11-1-11-1i−i
χ1011-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1ii−i−i1-1-111-11-111-1-1ii−i−i-11−ii-1-111−i−iiiiiiiiiii−i−i−i−i−i−i−i−ii−iii−i−i−ii-11−i−iii-1-111-11−iii−i11-1-1-11−ii
χ1111-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1ii−i−i1-1-111-11-111-1-1−i−iii1-1−ii11-1-1−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ii−i−iii−ii1-1−i−iii11-1-1-11i−i−ii-1-111-11i−i
χ1211-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1ii−i−i1-1-111-11-111-1-1−i−iii-11i−i-1-111ii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−i−iiii−i-11ii−i−i-1-1111-1−ii−ii-1-1111-1−ii
χ1311-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1−i−iii1-1-111-11-111-1-1ii−i−i1-1i−i11-1-1ii−i−i−i−i−i−i−i−i−i−iiiiiiiiii−iii−i−ii−i1-1ii−i−i11-1-1-11−iii−i-1-111-11−ii
χ1411-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1−i−iii1-1-111-11-111-1-1ii−i−i-11−ii-1-111−i−iii−i−i−i−i−i−i−i−iiiiiiiiii−iii−i−i−ii-11−i−iii-1-1111-1i−ii−i-1-1111-1i−i
χ1511-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1−i−iii1-1-111-11-111-1-1−i−iii1-1−ii11-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−i−iii−ii1-1−i−iii11-1-11-1−ii−ii11-1-11-1−ii
χ1611-1-1111-11-1-11-111-1-1-1111-1-1-1-1-111-11111-111-1-1-1-1−i−iii1-1-111-11-111-1-1−i−iii-11i−i-1-111ii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii−i−iiii−i-11ii−i−i-1-111-11i−i−ii11-1-1-11i−i
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-222220000000000000000000000000000-2-222220000000000000000-2-200000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000022-2-2-2-200000000000000002200000000
χ19222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1000000220000222222-1-1-1-1-1-122-1-1-1-1-1-1000000-1-100-1-1-1-100002200000000-1-100
χ20222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1000000-2-20000-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-1000000110011110000-2-2000000001100
χ21222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-10000002200002222-2-2111111-2-2111111000000-1-100-1-1-1-10000-2-2000000001100
χ22222222-1222-1-1-1222222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-1000000-2-20000-2-2-2-2-2-2111111-2-21111110000001100111100002200000000-1-100
χ2322222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-10000-1-100000000
χ2422222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111000000000000000022-1-1-1-1-2-2-2-2111111110000-1-100000000
χ2522222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-111110000000000000000-2-21111-2-2221111-1-1-1-100001100000000
χ2622222-122222222-1-1-12-12-1-1-122-12-1-1-122-1-12222220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2221111-1-1-1-10000000000000000-2-2111122-2-2-1-1-1-1111100001100000000
χ2722222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-11111111122220000−i3i3−i3i3−i3i3−i3i30000000000000000-2-2-1-1-1-10000−i3i3−i3i3−i3i3−i3i300001100000000
χ2822222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-11111111122220000i3−i3i3−i3i3−i3i3−i30000000000000000-2-2-1-1-1-10000i3−i3i3−i3i3−i3i3−i300001100000000
χ2922222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-20000−i3i3−i3i3i3−i3i3−i300000000000000002211110000i3−i3i3−i3−i3i3−i3i30000-1-100000000
χ3022222-12-2-222222-1-1-12-12-1-1-122-12-1-1-1-2-211-2-2-2-2-2-20000-1-1-1-111111111-2-2-2-20000i3−i3i3−i3−i3i3−i3i300000000000000002211110000−i3i3−i3i3i3−i3i3−i30000-1-100000000
χ312222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-10000220022220000-1-122-1-1-1-1-1-122-1-1-1-100000000-1-10000-1-1-1-1002200000000-1-1
χ322222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-10000-2-200-2-2-2-20000-1-122-1-1-1-1-1-122-1-1-1-100000000110000111100-2-20000000011
χ332222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1000022002222000011-2-2111111-2-2111100000000-1-10000-1-1-1-100-2-20000000011
χ342222-12222-1222-1222-1-1-12-1-1-1-12-122-12-122-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-10000-2-200-2-2-2-2000011-2-2111111-2-21111000000001100001111002200000000-1-1
χ3522-2-22222-2-2-22-222-2-2-2222-2-2-2-2-222-22-2-2-22-2-2222200002-2-22-22-22-2-2222i2i−2i−2i0000000000000000000000000000−2i2i2i2i−2i−2i0000000000000000−2i2i00000000
χ3622-2-22222-2-2-22-222-2-2-2222-2-2-2-2-222-22-2-2-22-2-2222200002-2-22-22-22-2-222−2i−2i2i2i00000000000000000000000000002i−2i−2i−2i2i2i00000000000000002i−2i00000000
χ3722-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-2112i2i−2i−2i-111-1-112-2-1-1110000002i−2i00002i2i−2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000−ii00−i−iii00002-200000000-1100
χ3822-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-2112i2i−2i−2i-111-1-112-2-1-111000000−2i2i0000−2i−2i2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000i−i00ii−i−i0000-22000000001-100
χ3922-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211−2i−2i2i2i-111-1-112-2-1-1110000002i−2i00002i2i−2i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000−ii00−i−iii0000-22000000001-100
χ4022-2-222-1-22-21-1122-2-2-22-1-1-2-2111-1-112-122-2-1-11-211−2i−2i2i2i-111-1-112-2-1-111000000−2i2i0000−2i−2i2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000i−i00ii−i−i00002-200000000-1100
χ4122-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-222220000-111-11-11-111-1-12i2i−2i−2i0000−i3i3i3−i33−3−330000000000000000−2i2i−i−iii00003−3−33−i3i3i3−i30000i−i00000000
χ4222-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-222220000-111-11-11-111-1-12i2i−2i−2i0000i3−i3−i3i3−333−30000000000000000−2i2i−i−iii0000−333−3i3−i3−i3i30000i−i00000000
χ4322-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-222220000-111-11-11-111-1-1−2i−2i2i2i0000−i3i3i3−i3−333−300000000000000002i−2iii−i−i0000−333−3−i3i3i3−i30000−ii00000000
χ4422-2-22-122-2-2-22-22-111-2-12-111-2-212-11-1-2-21-1-2-222220000-111-11-11-111-1-1−2i−2i2i2i0000i3−i3−i3i33−3−3300000000000000002i−2iii−i−i00003−3−33i3−i3−i3i30000−ii00000000
χ4522-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-20000-111-1-11-11-1-1112i2i−2i−2i2-22i−2i-1-111−i−iii00000000000000002i−2i−i−iii2i−2i2-2−i−iii-1-1110000−ii00000000
χ4622-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-20000-111-1-11-11-1-1112i2i−2i−2i-22−2i2i11-1-1ii−i−i00000000000000002i−2i−i−iii−2i2i-22ii−i−i11-1-10000−ii00000000
χ4722-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-20000-111-1-11-11-1-111−2i−2i2i2i2-2−2i2i-1-111ii−i−i0000000000000000−2i2iii−i−i−2i2i2-2ii−i−i-1-1110000i−i00000000
χ4822-2-22-12-22-2-22-22-111-2-12-111-2-212-11-122-1122-2-2-2-20000-111-1-11-11-1-111−2i−2i2i2i-222i−2i11-1-1−i−iii0000000000000000−2i2iii−i−i2i−2i-22−i−iii11-1-10000i−i00000000
χ4922-2-2-122-221-22-2-12-2-21-1-121111-2-12-2-12-12-2-1-1-21112i2i−2i−2i-111-12-2-11-1-11100002-20022-2-20000−i−i2i2i−i−i−i−iii−2i−2iiiii00000000-110000-1-111002i−2i00000000−ii
χ5022-2-2-122-221-22-2-12-2-21-1-121111-2-12-2-12-12-2-1-1-21112i2i−2i−2i-111-12-2-11-1-1110000-2200-2-2220000−i−i2i2i−i−i−i−iii−2i−2iiiii000000001-1000011-1-100−2i2i00000000i−i
χ5122-2-2-122-221-22-2-12-2-21-1-121111-2-12-2-12-12-2-1-1-2111−2i−2i2i2i-111-12-2-11-1-11100002-20022-2-20000ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000-110000-1-11100−2i2i00000000i−i
χ5222-2-2-122-221-22-2-12-2-21-1-121111-2-12-2-12-12-2-1-1-2111−2i−2i2i2i-111-12-2-11-1-1110000-2200-2-2220000ii−2i−2iiiii−i−i2i2i−i−i−i−i000000001-1000011-1-1002i−2i00000000−ii
χ532-22-2222002-2-22-2-2-22-22222-22-2-2-2-22-200000000002−22−222-2-2000000002i−2i2i−2i0000000000002−22−222−2−22−22−222−2−2002i−2i2i−2i000000000000000000−i2i2−i2i20000
χ542-22-2222002-2-22-2-2-22-22222-22-2-2-2-22-200000000002−22−222-2-200000000−2i2i−2i2i0000000000002−22−222−2−22−22−222−2−200−2i2i−2i2i000000000000000000i2−i2i2−i20000
χ552-22-2222002-2-22-2-2-22-22222-22-2-2-2-22-20000000000−22−2222-2-2000000002i−2i2i−2i000000000000−22−22−2−222−22−22−2−222002i−2i2i−2i000000000000000000i2−i2i2−i20000
χ562-22-2222002-2-22-2-2-22-22222-22-2-2-2-22-20000000000−22−2222-2-200000000−2i2i−2i2i000000000000−22−22−2−222−22−22−2−22200−2i2i−2i2i000000000000000000−i2i2−i2i20000
χ572-2-2222200-22-2-2-2-22-22222-22-222-2-2-2-20000000000−i2i2i2−i22-22-2000000002-2-22000000000000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2002-2-22000000000000000000−i2i2i2−i20000
χ582-2-2222200-22-2-2-2-22-22222-22-222-2-2-2-20000000000−i2i2i2−i22-22-200000000-222-2000000000000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i200-222-2000000000000000000i2−i2−i2i20000
χ592-2-2222200-22-2-2-2-22-22222-22-222-2-2-2-20000000000i2−i2−i2i22-22-2000000002-2-22000000000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2002-2-22000000000000000000i2−i2−i2i20000
χ602-2-2222200-22-2-2-2-22-22222-22-222-2-2-2-20000000000i2−i2−i2i22-22-200000000-222-2000000000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i200-222-2000000000000000000−i2i2i2−i20000
χ61444444-2-4-44-2-2-2444444-2-244-2-2-2-2-2-242-4-4-4222-4220000-2-2-2-222-4-422220000000000000000000000000000000000000000000000000000000000000000
χ6244444-2-2444-2-2-24-2-2-24-2-21-2-2-2-21-211-2-24-2-2-2-2-24-2-20000111111-2-21111000000440000-2-2-2-20000000000000000000000-2-2001111000000000000000000
χ6344444-2-2444-2-2-24-2-2-24-2-21-2-2-2-21-211-2-24-2-2-2-2-24-2-20000111111-2-21111000000-4-40000222200000000000000000000002200-1-1-1-1000000000000000000
χ6444444-2-2-4-44-2-2-24-2-2-24-2-21-2-2-2-21-211-22-422222-42200001111-1-122-1-1-1-1000000000000−2i32i3−2i32i300000000000000000000000000i3−i3i3−i3000000000000000000
χ6544444-2-2-4-44-2-2-24-2-2-24-2-21-2-2-2-21-211-22-422222-42200001111-1-122-1-1-1-10000000000002i3−2i32i3−2i300000000000000000000000000−i3i3−i3i3000000000000000000
χ664444-244-4-4-2444-2444-2-2-24-2-2-2-24-244-2-42-4-422-42220000-2-2-2-2-4-42222220000000000000000000000000000000000000000000000000000000000000000
χ674444-24-244-2-2-2-2-2444-2-21-2-2-211-21-2-2-2-2-24411-2-21144441111-2-2-2-211110000000000000000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000
χ684444-24-244-2-2-2-2-2444-2-21-2-2-211-21-2-2-2-2-24411-2-211-4-4-4-41111-2-2-2-2111100000000000000002222-1-1-1-12222-1-1-1-100000000000000000000000000000000
χ694444-24-2-4-4-2-2-2-2-2444-2-21-2-2-211-21-2-2-222-4-4-1-122-1-1000011112222-1-1-1-1000000000000000000003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000000000
χ704444-24-2-4-4-2-2-2-2-2444-2-21-2-2-211-21-2-2-222-4-4-1-122-1-1000011112222-1-1-1-100000000000000000000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000000000
χ714444-2-2444-2444-2-2-2-2-21-2-211-2-2-2-2-2-214-2-2-2-2-24-2-2-200001111-2-211111100004400-2-2-2-20000000000000000000000000000-2-20000111100000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.