Finite Group Databasebeta

← Group #11789724

Character table — Group #11789724

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order124422233444666612121212121236666666612121212121212121244442466666666661212121212121212121244888812121212121212128888242424242424242424242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111ii−i−i1-11111-1-11111-1-1-1-111-1-1-1-1i−i11-1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-1ii−i−ii−i
χ1011-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111ii−i−i1-11111-1-11111-1-1-1-111-1-1-1-1i−i-1-111iiii−i−i−i−ii−i-11ii−i−i-1-111-1-111−i−iii−ii
χ1111-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111ii−i−i-11-1-1-1-1-1-1-1-1-1-11111111111i−i11-1-1iiii−i−i−i−i−ii-11−i−iii11-1-1-1-111ii−i−i−ii
χ1211-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111ii−i−i-11-1-1-1-1-1-1-1-1-1-11111111111i−i-1-111iiii−i−i−i−i−ii1-1−i−iii-1-11111-1-1−i−iiii−i
χ1311-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111−i−iii1-11111-1-11111-1-1-1-111-1-1-1-1−ii11-1-1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-1−i−iii−ii
χ1411-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111−i−iii1-11111-1-11111-1-1-1-111-1-1-1-1−ii-1-111−i−i−i−iiiii−ii-11−i−iii-1-111-1-111ii−i−ii−i
χ1511-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111−i−iii-11-1-1-1-1-1-1-1-1-1-11111111111−ii11-1-1−i−i−i−iiiiii−i-11ii−i−i11-1-1-1-111−i−iiii−i
χ1611-1-11-1-111-1111111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-111−i−iii-11-1-1-1-1-1-1-1-1-1-11111111111−ii-1-111−i−i−i−iiiiii−i1-1ii−i−i-1-11111-1-1ii−i−i−ii
χ1722222222-1222222-122-1-122-1-12-1-1-1-1-1222-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10022220000000000220000-1-1-1-1-1-1-1-1000000
χ1822222222-1222222-122-1-122-1-12-1-1-1-1-1222-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-2-2-20000000000-2-2000011111111000000
χ1922222222-1222222-122-1-122-1-12-1-1-1-1-1222-1-1-1-1-1-1-10000-2-2-2-211-1-11111-2-211-1-111110022220000000000-2-20000-1-1-1-11111000000
χ2022222222-1222222-122-1-122-1-12-1-1-1-1-1222-1-1-1-1-1-1-10000-2-2-2-211-1-11111-2-211-1-1111100-2-2-2-200000000002200001111-1-1-1-1000000
χ212222222-12222-1-1-12-1-122-1-1-12-122-1-1-1-1-1-12-1-1-1-122222222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1220000-1-1-1-1-1-1-1-12200-1-1-1-100000000000000
χ222222222-12222-1-1-12-1-122-1-1-12-122-1-1-1-1-1-12-1-1-1-1222222-2-211-2-2-1-1111111-2-2-1-11111220000-1-1-1-1-1-1-1-1-2-200111100000000000000
χ232222222-12222-1-1-12-1-122-1-1-12-122-1-1-1-1-1-12-1-1-1-122-2-2-2-222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2000011111111-2-200111100000000000000
χ242222222-12222-1-1-12-1-122-1-1-12-122-1-1-1-1-1-12-1-1-1-122-2-2-2-2-2-211-2-2-1-1111111-2-2-1-11111-2-20000111111112200-1-1-1-100000000000000
χ2522222-2-2222-2-2222222222222-2-2-2222-2-2-222222-2-20000000000-2-200000000-2-20000002i−2i2i−2i00000000000000002i−2i2i−2i0000000000
χ2622222-2-2222-2-2222222222222-2-2-2222-2-2-222222-2-20000000000-2-200000000-2-2000000−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000
χ2722222-2-22-12-2-2222-122-1-122-1-1-211-1-1-1-2-2-2-1-1-1-1-11100000000−i3i311−i3−i3i3i300−i3i311−i3−i3i3i3002i−2i2i−2i0000000000000000−ii−ii3−33−3000000
χ2822222-2-22-12-2-2222-122-1-122-1-1-211-1-1-1-2-2-2-1-1-1-1-11100000000−i3i311−i3−i3i3i300−i3i311−i3−i3i3i300−2i2i−2i2i0000000000000000i−ii−i−33−33000000
χ2922222-2-22-12-2-2222-122-1-122-1-1-211-1-1-1-2-2-2-1-1-1-1-11100000000i3−i311i3i3−i3−i300i3−i311i3i3−i3−i3002i−2i2i−2i0000000000000000−ii−ii−33−33000000
χ3022222-2-22-12-2-2222-122-1-122-1-1-211-1-1-1-2-2-2-1-1-1-1-11100000000i3−i311i3i3−i3−i300i3−i311i3i3−i3−i300−2i2i−2i2i0000000000000000i−ii−i3−33−3000000
χ312222-22-222-22-2-2-222-2-222222-2-22-2-2-2222-2-222-2-22-222220000002-2000000002-20000-2-2000022-2-222-2-20000000000000000000000
χ322222-22-222-22-2-2-222-2-222222-2-22-2-2-2222-2-222-2-22-2-2-2-2-20000002-2000000002-20000220000-2-222-2-2220000000000000000000000
χ332222-22-2-12-22-211-121122-1-1-1-212-211-1-1-11-2-1-1112-2222200−i3i300-11−i3i3−i3i3−i3i300-11−i3i3−i3i3-2-20000-1-111-1-1110000−i3i3−i3i300000000000000
χ342222-22-2-12-22-211-121122-1-1-1-212-211-1-1-11-2-1-1112-2222200i3−i300-11i3−i3i3−i3i3−i300-11i3−i3i3−i3-2-20000-1-111-1-1110000i3−i3i3−i300000000000000
χ352222-22-2-12-22-211-121122-1-1-1-212-211-1-1-11-2-1-1112-2-2-2-2-200−i3i300-11−i3i3−i3i3−i3i300-11−i3i3−i3i322000011-1-111-1-10000i3−i3i3−i300000000000000
χ362222-22-2-12-22-211-121122-1-1-1-212-211-1-1-11-2-1-1112-2-2-2-2-200i3−i300-11i3−i3i3−i3i3−i300-11i3−i3i3−i322000011-1-111-1-10000−i3i3−i3i300000000000000
χ372222-2-2222-2-22-2-222-2-222222-22-22-2-22-2-22-222-2-2-220000000000-2200000000-2200000000000000000000000000000000002-22-200
χ382222-2-2222-2-22-2-222-2-222222-22-22-2-22-2-22-222-2-2-220000000000-2200000000-220000000000000000000000000000000000-22-2200
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200000000002200000000-2-20000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200000000002200000000-2-2000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000
χ4122-2-22222-1-2-2-2222-1-2-211-2-2-1-12-1-1-1-1-12-2-2111111100000000−i3i3-1-1−i3−i3i3i300i3−i311i3i3−i3−i3002i−2i−2i2i0000000000000000−iii−i3−3−33000000
χ4222-2-22222-1-2-2-2222-1-2-211-2-2-1-12-1-1-1-1-12-2-2111111100000000−i3i3-1-1−i3−i3i3i300i3−i311i3i3−i3−i300−2i2i2i−2i0000000000000000i−i−ii−333−3000000
χ4322-2-22222-1-2-2-2222-1-2-211-2-2-1-12-1-1-1-1-12-2-2111111100000000i3−i3-1-1i3i3−i3−i300−i3i311−i3−i3i3i3002i−2i−2i2i0000000000000000−iii−i−333−3000000
χ4422-2-22222-1-2-2-2222-1-2-211-2-2-1-12-1-1-1-1-12-2-2111111100000000i3−i3-1-1i3i3−i3−i300−i3i311−i3−i3i3i300−2i2i2i−2i0000000000000000i−i−ii3−3−33000000
χ4522-2-22-2-22-1-222222-1-2-211-2-2-1-1-211-1-1-1-22211111-1-100002-222-1-111-1-1-1-1-2-211-1-111110022-2-200000000002-20000-1-111-1-111000000
χ4622-2-22-2-22-1-222222-1-2-211-2-2-1-1-211-1-1-1-22211111-1-100002-222-1-111-1-1-1-1-2-211-1-1111100-2-2220000000000-22000011-1-111-1-1000000
χ4722-2-22-2-22-1-222222-1-2-211-2-2-1-1-211-1-1-1-22211111-1-10000-22-2-21111111122-1-1-1-1-1-1-1-10022-2-20000000000-220000-1-11111-1-1000000
χ4822-2-22-2-22-1-222222-1-2-211-2-2-1-1-211-1-1-1-22211111-1-10000-22-2-21111111122-1-1-1-1-1-1-1-100-2-22200000000002-2000011-1-1-1-111000000
χ4922-2-22-2-2-12-222-1-1-1211-2-211-121-2-2-1-1-11-1-1-21111222i2i−2i−2i2-2-1-12211-1-1-1-111-2-2-1-111112i−2i0000−i−i−i−iiiii2i−2i00−i−iii00000000000000
χ5022-2-22-2-2-12-222-1-1-1211-2-211-121-2-2-1-1-11-1-1-21111222i2i−2i−2i-2211-2-2111111-1-122-1-1-1-1-1-12i−2i0000−i−i−i−iiiii−2i2i00ii−i−i00000000000000
χ5122-2-22-2-2-12-222-1-1-1211-2-211-121-2-2-1-1-11-1-1-2111122−2i−2i2i2i2-2-1-12211-1-1-1-111-2-2-1-11111−2i2i0000iiii−i−i−i−i−2i2i00ii−i−i00000000000000
χ5222-2-22-2-2-12-222-1-1-1211-2-211-121-2-2-1-1-11-1-1-2111122−2i−2i2i2i-2211-2-2111111-1-122-1-1-1-1-1-1−2i2i0000iiii−i−i−i−i2i−2i00−i−iii00000000000000
χ5322-2-2-22-2222-22-2-22222-2-2-2-22-2-22-2-2-222-222-2-222-2200000000002-200000000-2200000000000000000000000000000000002i−2i−2i2i00
χ5422-2-2-22-2222-22-2-22222-2-2-2-22-2-22-2-2-222-222-2-222-2200000000002-200000000-220000000000000000000000000000000000−2i2i2i−2i00
χ5522-2-2-2-222222-2-2-22222-2-2-2-22-22-22-2-22-22-22-2-2222-22i2i−2i−2i000000-22000000002-20000−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ5622-2-2-2-222222-2-2-22222-2-2-2-22-22-22-2-22-22-22-2-2222-2−2i−2i2i2i000000-22000000002-200002i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
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χ6022-2-2-2-22-1222-211-12-1-1-2-211-1-2-1-2211-11-11211-1-12-2−2i−2i2i2i00i3−i3001-1i3−i3i3−i3−i3i300-11−i3i3−i3i32i−2i0000ii−i−i−i−iii00003−3−3300000000000000
χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-21111-2-2000044-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
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χ864-44i−4i0004400000-4-4004i−4i4i−4i4000000-400004i−4i0000−2−2i2+2i−2+2i2−2i0000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ874-44i−4i000-24000−2i32i32-423−234i−4i−2i2i-20000−2i32i320000−2i2i23−23002+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−1+i1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ884-44i−4i000-24000−2i32i32-423−234i−4i−2i2i-20000−2i32i320000−2i2i23−2300−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ111−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ894-44i−4i000-240002i3−2i32-4−23234i−4i−2i2i-200002i3−2i320000−2i2i−2323002+2i−2−2i2−2i−2+2i0000000000000000000000000000−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ904-44i−4i000-240002i3−2i32-4−23234i−4i−2i2i-200002i3−2i320000−2i2i−232300−2−2i2+2i−2+2i2−2i00000000000000000000000000001+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ111−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ914-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000−4i4i00002−2i−2+2i2+2i−2−2i00000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ924-4−4i4i0004400000-4-400−4i4i−4i4i4000000-40000−4i4i0000−2+2i2−2i−2−2i2+2i0000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ934-4−4i4i000-24000−2i32i32-4−2323−4i4i2i−2i-20000−2i32i3200002i−2i−2323002−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−1−i1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ944-4−4i4i000-24000−2i32i32-4−2323−4i4i2i−2i-20000−2i32i3200002i−2i−232300−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ111+i−1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ954-4−4i4i000-240002i3−2i32-423−23−4i4i2i−2i-200002i3−2i3200002i−2i23−23002−2i−2+2i2+2i−2−2i0000000000000000000000000000−1+i1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−1−i1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ964-4−4i4i000-240002i3−2i32-423−23−4i4i2i−2i-200002i3−2i3200002i−2i23−2300−2+2i2−2i−2−2i2+2i00000000000000000000000000001−i−1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111+i−1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ978-88i−8i0008-400000-8400−4i4i8i−8i-400000040000−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i34443−43−4i4i−4i4i200002i3−2i3-200002i−2i−23230000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4343−4i4i−4i4i20000−2i32i3-200002i−2i23−230000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-84004i−4i−8i8i-4000000400004i−4i000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i344−43434i−4i4i−4i200002i3−2i3-20000−2i2i23−230000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i34443−434i−4i4i−4i20000−2i32i3-20000−2i2i−23230000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.