Finite Group Databasebeta

← Group #11775614

Character table — Group #11775614

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222444444444444444444444888888888888888888888818181818181824242424242424242424242424242424363636363648484848
order1222223344666666346666666888812121212121212126612121212242424242424242424242424242424242222444444444412121212121212124888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-1-1-1-1-11-11
χ51111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ61111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ71111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-111111-11-1
χ81111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-11111-11-11
χ91111-1-111-1-111111111-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1i−ii−iii−i−iii−i−i-1ii−i−i11-1-1
χ101111-1-111-1-111111111-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-111−ii−ii−i−iii−i−iii-1ii−i−i-1-111
χ111111-1-111-1-111111111-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-11-1-11i−i−iiii−i−i−i−iii1−i−iii1-1-11
χ121111-1-111-1-111111111-1-1111-1-1ii−i−i-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-111-1−iii−i−i−iiiii−i−i1−i−iii-111-1
χ131111-1-111-1-111111111-1-1111-1-1−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1−ii−ii−i−iii−i−iii-1−i−iii11-1-1
χ141111-1-111-1-111111111-1-1111-1-1−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-111i−ii−iii−i−iii−i−i-1−i−iii-1-111
χ151111-1-111-1-111111111-1-1111-1-1−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-11-1-11−iii−i−i−iiiii−i−i1ii−i−i1-1-11
χ161111-1-111-1-111111111-1-1111-1-1−i−iii-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-111-1i−i−iiii−i−i−i−iii1ii−i−i-111-1
χ1722222222-2-22222222-222222220000-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-20000000000000000-200000000
χ1822222222-2-22222222-222222220000-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2220000000000000000200000000
χ192222222-1222-12-12-1-122-1-1-1-12-1222222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000020200220000-1-1-1-1000000-10-1
χ202222222-1222-12-12-1-122-1-1-1-12-1222222-1-1-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000-20-200-2-200001111000000101
χ212222222-1222-12-12-1-122-1-1-1-12-1-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-2-2111111-2-2111111000000020200-2-200001111000000-10-1
χ222222222-1222-12-12-1-122-1-1-1-12-1-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000000-20-200220000-1-1-1-1000000101
χ23222222-1222-12-12-12-12-12-1-1-1-122222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000020202200-1-1-1-1000000000-10-10
χ24222222-1222-12-12-12-12-12-1-1-1-122222-1-122-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000-20-20-2-20011110000000001010
χ25222222-1222-12-12-12-12-12-1-1-1-12-2-2-2-2-1-122-1-1-1-1-1-1-12-1-111-2-2111111-2-211110000002020-2-2001111000000000-10-10
χ26222222-1222-12-12-12-12-12-1-1-1-12-2-2-2-2-1-122-1-1-1-1-1-1-12-1-111-2-2111111-2-21111000000-20-202200-1-1-1-10000000001010
χ272222-2-222222222222-2-2-2222-2-2000022222222-2-2-2-2-2-2000000000000000022-2-2-2-20000000000000000200000000
χ282222-2-222222222222-2-2-2222-2-2000022222222-2-2-2-2-2-20000000000000000-2-222220000000000000000-200000000
χ292222-2-22-1-2-22-12-12-1-12-21-1-1-1-212i2i−2i−2i-2-2111111112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000000020-2002i−2i0000−i−iii000000-101
χ302222-2-22-1-2-22-12-12-1-12-21-1-1-1-212i2i−2i−2i-2-2111111112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000000-20200−2i2i0000ii−i−i00000010-1
χ312222-2-22-1-2-22-12-12-1-12-21-1-1-1-21−2i−2i2i2i-2-2111111112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000000020-200−2i2i0000ii−i−i000000-101
χ322222-2-22-1-2-22-12-12-1-12-21-1-1-1-21−2i−2i2i2i-2-2111111112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000-202002i−2i0000−i−iii00000010-1
χ332222-2-2-12-2-2-12-12-12-121-2-1-1-11-22i2i−2i−2i11-2-2111111-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00000020-202i−2i00−i−iii000000000-1010
χ342222-2-2-12-2-2-12-12-12-121-2-1-1-11-22i2i−2i−2i11-2-2111111-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii000000-2020−2i2i00ii−i−i00000000010-10
χ352222-2-2-12-2-2-12-12-12-121-2-1-1-11-2−2i−2i2i2i11-2-2111111-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00000020-20−2i2i00ii−i−i000000000-1010
χ362222-2-2-12-2-2-12-12-12-121-2-1-1-11-2−2i−2i2i2i11-2-2111111-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i000000-20202i−2i00−i−iii00000000010-10
χ3722-2-22-2220022-2-2-2-220222-2-2-2-22−22−2000000002-200002−22−222−2−22−22−222−2−22-22-200000000000000000002−22−20000
χ3822-2-22-2220022-2-2-2-220222-2-2-2-22−22−2000000002-200002−22−222−2−22−22−222−2−2-22-220000000000000000000−22−220000
χ3922-2-22-2220022-2-2-2-220222-2-2-2-2−22−22000000002-20000−22−22−2−222−22−22−2−2222-22-20000000000000000000−22−220000
χ4022-2-22-2220022-2-2-2-220222-2-2-2-2−22−22000000002-20000−22−22−2−222−22−22−2−222-22-2200000000000000000002−22−20000
χ4122-2-2-22220022-2-2-2-220-2-22-2-222−i2i2i2−i200000000-220000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i22-2-220000000000000000000−i2i2i2−i20000
χ4222-2-2-22220022-2-2-2-220-2-22-2-222−i2i2i2−i200000000-220000−i2i2−i2i2−i2−i2i2i2i2−i2i2−i2i2i2−i2−i2-222-20000000000000000000i2−i2−i2i20000
χ4322-2-2-22220022-2-2-2-220-2-22-2-222i2−i2−i2i200000000-220000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i22-2-220000000000000000000i2−i2−i2i20000
χ4422-2-2-22220022-2-2-2-220-2-22-2-222i2−i2−i2i200000000-220000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2-222-20000000000000000000−i2i2i2−i20000
χ454444444-2-4-44-24-24-2-2-44-2-2-2-24-20000-4-4222222-2-2-422200000000000000000000000000000000000000000000000
χ46444444-24-4-4-24-24-24-2-4-24-2-2-2-24000022-4-42222-2-22-42200000000000000000000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2111-2-24444-2-2-2-2111111-2-211-2-2-2-21111-2-2-2-211110000000000000000000000000000000
χ48444444-2-244-2-2-2-2-2-214-2-2111-2-2-4-4-4-4-2-2-2-2111111-2-2112222-1-1-1-12222-1-1-1-10000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-200002222-1-1-1-11122-1-100003i−3i3i−3i00003i−3i3i−3i0000000000000000000000000000000
χ50444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-200002222-1-1-1-11122-1-10000−3i3i−3i3i0000−3i3i−3i3i0000000000000000000000000000000
χ514444-4-44-2444-24-24-2-2-4-42-2-2-2-42000044-2-2-2-2-2-222-422200000000000000000000000000000000000000000000000
χ524444-4-4-2444-24-24-24-2-42-4-2-2-22-40000-2-244-2-2-2-2222-42200000000000000000000000000000000000000000000000
χ534444-4-4-2-244-2-2-2-2-2-21-422111220000-2-2-2-21111-1-122-1-100003-33-30000-33-330000000000000000000000000000000
χ544444-4-4-2-244-2-2-2-2-2-21-422111220000-2-2-2-21111-1-122-1-10000-33-3300003-33-30000000000000000000000000000000
χ554444-4-4-2-2-4-4-2-2-2-2-2-21422111224i4i−4i−4i2222-1-1-1-1-1-1-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000
χ564444-4-4-2-2-4-4-2-2-2-2-2-2142211122−4i−4i4i4i2222-1-1-1-1-1-1-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000
χ5744-4-44-44-2004-2-42-42-204-2-222-4222−2222−2200000000-22000022−22−22−2−22222−22−22−2−2220000000000000000000000000000000
χ5844-4-44-44-2004-2-42-42-204-2-222-42−2222−222200000000-220000−22222−222−2−2−22222−222−2−20000000000000000000000000000000
χ5944-4-44-4-2400-242-42-4-20-24-2222-422−2222−2200000000-220000−2222−22−2−222−2222−22−2−2220000000000000000000000000000000
χ6044-4-44-4-2400-242-42-4-20-24-2222-4−2222−222200000000-2200002−2−222222−2−22−2−222222−2−20000000000000000000000000000000
χ6144-4-44-4-2-200-2-2222210-2-21-1-12222−2222−2200003i3i−3i−3i1-1003i−3i−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ230000000000000000000000000000000
χ6244-4-44-4-2-200-2-2222210-2-21-1-12222−2222−220000−3i−3i3i3i1-100−3i3i−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ230000000000000000000000000000000
χ6344-4-44-4-2-200-2-2222210-2-21-1-122−2222−222200003i3i−3i−3i1-1003i−3i2−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ230000000000000000000000000000000
χ6444-4-44-4-2-200-2-2222210-2-21-1-122−2222−22220000−3i−3i3i3i1-100−3i3i2−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ232−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ230000000000000000000000000000000
χ6544-4-4-444-2004-2-42-42-20-42-2224-2−2i22i22i2−2i2000000002-20000−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000000
χ6644-4-4-444-2004-2-42-42-20-42-2224-22i2−2i2−2i22i2000000002-200002i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000000
χ6744-4-4-44-2400-242-42-4-202-4-222-24−2i22i22i2−2i2000000002-20000i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000000
χ6844-4-4-44-2400-242-42-4-202-4-222-242i2−2i2−2i22i2000000002-20000−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000000
χ6944-4-4-44-2-200-2-2222210221-1-1-2-2−2i22i22i2−2i200003i3i−3i−3i-1100−3i3ii2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000000000000000
χ7044-4-4-44-2-200-2-2222210221-1-1-2-2−2i22i22i2−2i20000−3i−3i3i3i-11003i−3ii2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000000000000000
χ7144-4-4-44-2-200-2-2222210221-1-1-2-22i2−2i2−2i22i200003i3i−3i−3i-1100−3i3i−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000000000
χ7244-4-4-44-2-200-2-2222210221-1-1-2-22i2−2i2−2i22i20000−3i−3i3i3i-11003i−3i−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000000000000000
χ734-44-400444i−4i-4-444-4-44000-44-40000004i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000
χ744-44-40044−4i4i-4-444-4-44000-44-4000000−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000
χ754-44-4004-24i−4i-424-2-42-20002-220000004i−4i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000
χ764-44-4004-24i−4i-424-2-42-20002-220000004i−4i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000
χ774-44-4004-2−4i4i-424-2-42-20002-22000000−4i4i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000
χ784-44-4004-2−4i4i-424-2-42-20002-22000000−4i4i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000
χ794-44-400-244i−4i2-4-242-4-20002-22000000−2i2i4i−4i−2i2i−2i2i000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000
χ804-44-400-244i−4i2-4-242-4-20002-22000000−2i2i4i−4i−2i2i−2i2i000000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000
χ814-44-400-24−4i4i2-4-242-4-20002-220000002i−2i−4i4i2i−2i2i−2i000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000
χ824-44-400-24−4i4i2-4-242-4-20002-220000002i−2i−4i4i2i−2i2i−2i000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000
χ834-4-44004400-4-4-4-4444000-4-4400000000000000000000000000000000000000004-40000000000000000000000000
χ844-4-44004400-4-4-4-4444000-4-440000000000000000000000000000000000000000-440000000000000000000000000
χ858-88-800-4-48i−8i44-4-4442000-22-2000000−4i4i−4i4i2i−2i2i−2i00000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−8i8i44-4-4442000-22-20000004i−4i4i−4i−2i2i−2i2i00000000000000000000000000000000000000000000000000000
χ878-8-88008-400-84-848-4-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ888-8-8800-48004-84-8-48-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-4-4004444-4-42000-2-2200000000006-6-6600000000000000000000000000000000000000000000000000000
χ908-8-8800-4-4004444-4-42000-2-220000000000-666-600000000000000000000000000000000000000000000000000000

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