Finite Group Databasebeta

← Group #11775907

Character table — Group #11775907

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222244444444444444466666666668888888888888121212121212121212121216161616161624242424242424242424242424242424363636367272
order12223344446666663466612121212121212121212224444121212124412121212121212121212124668888121212121212121212124488121212122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-11-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111111-1111-1-111-1-1-1-1-111ii−i−i-1-1-1-11-111-1-11-1i−i11-1-1ii−i−iii−i−iii−i−ii−i
χ10111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111111-1111-1-111-1-1-1-1-111−i−iii-1-1-1-11-111-1-11-1−ii11-1-1−i−iii−i−iii−i−iii−ii
χ11111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-11111-111-1-11111-1-1-1-1-111ii−i−i-1-1-1-1-11-1-111-11−ii-1-111ii−i−i−i−iiiii−i−i−ii
χ12111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-11111-111-1-11111-1-1-1-1-111−i−iii-1-1-1-1-11-1-111-11i−i-1-111−i−iiiii−i−i−i−iiii−i
χ13111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111-1-111-1-1-1-11-1-1ii−i−i11111-111-1-1-11i−i-1-111ii−i−iii−i−i−i−iii−ii
χ14111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111-1-111-1-1-1-11-1-1−i−iii11111-111-1-1-11−ii-1-111−i−iii−i−iiiii−i−ii−i
χ15111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-11-1-1ii−i−i1111-11-1-1111-1−ii11-1-1ii−i−i−i−iii−i−iiii−i
χ16111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-11-1-1−i−iii1111-11-1-1111-1i−i11-1-1−i−iiiii−i−iii−i−i−ii
χ1722222222-2-22222222-2222-2-222-2-222-2-222-2-222-2-2-2-200-20000-2-222-2-2-222000022-2-20000000000000000000000000000
χ1822222222-2-22222222-2222-2-222-2-222-2-2-2-222-2-2222200-20000-2-222-2-22-2-20000-2-2220000000000000000000000000000
χ19222222-2-2222222222-2222-2-2-2-222-2-22222-2-2-2-2-2-2-2-200-20000-2-2-2-2222220000-2-2220000000000000000000000000000
χ20222222-2-2222222222-2222-2-2-2-222-2-222-2-22222222200-20000-2-2-2-222-2-2-2000022-2-20000000000000000000000000000
χ2122222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222222222-1-1-1-1222-1-1-1-1-1-1-1-1-1-12-1-10000-1-1-1-122-1-1-1-12200-1-1-1-100000000000000
χ2222222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-221111-1-1-1-1-1-12-1-10000-1-1-1-1-2-21111-2-200111100000000000000
χ2322222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-21111222-1-1-1-1-1-1-1-1-1-1-2110000111122-1-1-1-1-2-200111100000000000000
χ2422222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-21111-2-221111-1-1-1-1-1-1-21100001111-2-211112200-1-1-1-100000000000000
χ2522222-122-2-2222-1-1-1-1-2-1-1-111-1-11122-2-222-2-222111100-2−i3i3−i3i311-1-111-2-1-10000-1-11100−i3i3−i3i30000−i3i3−i3i300000000000000
χ2622222-122-2-2222-1-1-1-1-2-1-1-111-1-11122-2-222-2-222111100-2i3−i3i3−i311-1-111-2-1-10000-1-11100i3−i3i3−i30000i3−i3i3−i300000000000000
χ2722222-122-2-2222-1-1-1-1-2-1-1-111-1-11122-2-2-2-222-2-2-1-1-1-100-2−i3i3−i3i311-1-111211000011-1-100−i3i3−i3i30000i3−i3i3−i300000000000000
χ2822222-122-2-2222-1-1-1-1-2-1-1-111-1-11122-2-2-2-222-2-2-1-1-1-100-2i3−i3i3−i311-1-111211000011-1-100i3−i3i3−i30000−i3i3−i3i300000000000000
χ2922222-1-2-222222-1-1-1-1-2-1-1-11111-1-1-2-22222-2-2-2-2111100-2−i3i3i3−i31111-1-12-1-1000011-1-100−i3i3i3−i30000−i3i3i3−i300000000000000
χ3022222-1-2-222222-1-1-1-1-2-1-1-11111-1-1-2-22222-2-2-2-2111100-2i3−i3−i3i31111-1-12-1-1000011-1-100i3−i3−i3i30000i3−i3−i3i300000000000000
χ3122222-1-2-222222-1-1-1-1-2-1-1-11111-1-1-2-222-2-22222-1-1-1-100-2−i3i3i3−i31111-1-1-2110000-1-11100−i3i3i3−i30000i3−i3−i3i300000000000000
χ3222222-1-2-222222-1-1-1-1-2-1-1-11111-1-1-2-222-2-22222-1-1-1-100-2i3−i3−i3i31111-1-1-2110000-1-11100i3−i3−i3i30000−i3i3i3−i300000000000000
χ3322222-1-2-2-2-2222-1-1-1-12-1-1-1-1-11111-2-2-2-22222-2-2-1-1-1-12-22-1-111-1-11111-2-1-1000011112-2-1-1112-200-1-11100000000000000
χ3422222-1-2-2-2-2222-1-1-1-12-1-1-1-1-11111-2-2-2-22222-2-2-1-1-1-1-22211-1-1-1-11111-2-1-100001111-2211-1-1-220011-1-100000000000000
χ3522222-1-2-2-2-2222-1-1-1-12-1-1-1-1-11111-2-2-2-2-2-2-2-22211112-22-1-111-1-111112110000-1-1-1-12-2-1-111-220011-1-100000000000000
χ3622222-1-2-2-2-2222-1-1-1-12-1-1-1-1-11111-2-2-2-2-2-2-2-2221111-22211-1-1-1-111112110000-1-1-1-1-2211-1-12-200-1-11100000000000000
χ372222-122222-1-1-1222-12-1-1-1222222-1-1-1-1000000000022-12222-1-1-1-1-1-100022220000-1-1-1-1-1-100220000-1-1-1-1-1-1-1-1000000
χ382222-122222-1-1-1222-12-1-1-1222222-1-1-1-1000000000022-12222-1-1-1-1-1-1000-2-2-2-20000-1-1-1-1-1-100-2-2000011111111000000
χ392222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000000000-2-2-1-2-2-2-2-1-1-1-1-1-10002222000011111100-2-20000-1-1-1-11111000000
χ402222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000000000-2-2-1-2-2-2-2-1-1-1-1-1-1000-2-2-2-20000111111002200001111-1-1-1-1000000
χ412222-12-2-2-2-2-1-1-1222-12-1-1-122-2-2-2-2111100000000002-2-122-2-2-1-111110002i2i−2i−2i0000-11-1-111002i−2i0000−i−iii−i−iii000000
χ422222-12-2-2-2-2-1-1-1222-12-1-1-122-2-2-2-2111100000000002-2-122-2-2-1-11111000−2i−2i2i2i0000-11-1-11100−2i2i0000ii−i−iii−i−i000000
χ432222-12-2-2-2-2-1-1-1222-12-1-1-122-2-2-2-211110000000000-22-1-2-222-1-111110002i2i−2i−2i00001-111-1-100−2i2i0000−i−iiiii−i−i000000
χ442222-12-2-2-2-2-1-1-1222-12-1-1-122-2-2-2-211110000000000-22-1-2-222-1-11111000−2i−2i2i2i00001-111-1-1002i−2i0000ii−i−i−i−iii000000
χ452-22-222002i−2i-22-2-22-220-22-200002i−2i002i−2i002i−2i2-22i2i−2i−2i000000000002i−2i0001+i−1−i1−i−1+i2-200000000000000001+i−1−i1−i−1+i00001−i−1+i1+i−1−i00
χ462-22-222002i−2i-22-2-22-220-22-200002i−2i002i−2i002i−2i2-22i2i−2i−2i000000000002i−2i000−1−i1+i−1+i1−i2-20000000000000000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i00
χ472-22-222002i−2i-22-2-22-220-22-200002i−2i002i−2i00−2i2i-22−2i−2i2i2i000000000002i−2i0001+i−1−i1−i−1+i-2200000000000000001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i00
χ482-22-222002i−2i-22-2-22-220-22-200002i−2i002i−2i00−2i2i-22−2i−2i2i2i000000000002i−2i000−1−i1+i−1+i1−i-220000000000000000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i00
χ492-22-22200−2i2i-22-2-22-220-22-20000−2i2i00−2i2i002i−2i-222i2i−2i−2i00000000000−2i2i0001−i−1+i1+i−1−i-2200000000000000001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i00
χ502-22-22200−2i2i-22-2-22-220-22-20000−2i2i00−2i2i002i−2i-222i2i−2i−2i00000000000−2i2i000−1+i1−i−1−i1+i-220000000000000000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i00
χ512-22-22200−2i2i-22-2-22-220-22-20000−2i2i00−2i2i00−2i2i2-2−2i−2i2i2i00000000000−2i2i0001−i−1+i1+i−1−i2-200000000000000001−i−1+i1+i−1−i00001+i−1−i1−i−1+i00
χ522-22-22200−2i2i-22-2-22-220-22-20000−2i2i00−2i2i00−2i2i2-2−2i−2i2i2i00000000000−2i2i000−1+i1−i−1−i1+i2-20000000000000000−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i00
χ534444-2444-4-4-2-2-2444-2-4-2-2-2-4-444-4-4-2-2220000000000002000022-2-222000000000000000000000000000000000000000
χ544444-24-4-444-2-2-2444-2-4-2-2-2-4-4-4-44422-2-2000000000000200002222-2-2000000000000000000000000000000000000000
χ554444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-2000000000044-2-2-2-2-211111100000000000-2-211110000000000000000000000
χ564444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-20000000000-4-4-222221111110000000000022-1-1-1-10000000000000000000000
χ574444-2-244-4-4-2-2-2-2-2-21-411122-2-222-2-2220000000000002−2i32i3−2i32i3-1-111-1-10000000000000i3−i3i3−i30000000000000000000000
χ584444-2-244-4-4-2-2-2-2-2-21-411122-2-222-2-22200000000000022i3−2i32i3−2i3-1-111-1-10000000000000−i3i3−i3i30000000000000000000000
χ594444-2-2-4-444-2-2-2-2-2-21-41112222-2-222-2-20000000000002−2i32i32i3−2i3-1-1-1-1110000000000000i3−i3−i3i30000000000000000000000
χ604444-2-2-4-444-2-2-2-2-2-21-41112222-2-222-2-200000000000022i3−2i3−2i32i3-1-1-1-1110000000000000−i3i3i3−i30000000000000000000000
χ614444-2-2-4-4-4-4-2-2-2-2-2-214111-2-22222222200000000004-4-2-2-22211-1-1-1-100000000000-2211-1-10000000000000000000000
χ624444-2-2-4-4-4-4-2-2-2-2-2-214111-2-2222222220000000000-44-222-2-211-1-1-1-1000000000002-2-1-1110000000000000000000000
χ6344-4-44400004-4-44-4-4404-4-400000000004-400000000000000000000004-4000000000000000000000000000000000000
χ6444-4-44400004-4-44-4-4404-4-40000000000-440000000000000000000000-44000000000000000000000000000000000000
χ6544-4-44-200004-4-4-222-20-222−2i32i3000000004-40000−2i32i3−2i32i30000000−2i32i300000-22000000000000000000000000000000000000
χ6644-4-44-200004-4-4-222-20-222−2i32i300000000-4400002i3−2i32i3−2i30000000−2i32i3000002-2000000000000000000000000000000000000
χ6744-4-44-200004-4-4-222-20-2222i3−2i3000000004-400002i3−2i32i3−2i300000002i3−2i300000-22000000000000000000000000000000000000
χ6844-4-44-200004-4-4-222-20-2222i3−2i300000000-440000−2i32i3−2i32i300000002i3−2i3000002-2000000000000000000000000000000000000
χ694-44-44-2004i−4i-44-42-22-202-220000−2i2i004i−4i004i−4i4-4−2i−2i2i2i00000000000−2i2i0000000-22000000000000000000000000000000
χ704-44-44-2004i−4i-44-42-22-202-220000−2i2i004i−4i00−4i4i-442i2i−2i−2i00000000000−2i2i00000002-2000000000000000000000000000000
χ714-44-44-200−4i4i-44-42-22-202-2200002i−2i00−4i4i004i−4i-44−2i−2i2i2i000000000002i−2i00000002-2000000000000000000000000000000
χ724-44-44-200−4i4i-44-42-22-202-2200002i−2i00−4i4i00−4i4i4-42i2i−2i−2i000000000002i−2i0000000-22000000000000000000000000000000
χ734-44-4-24004i−4i2-22-44-4-202-2200004i−4i00−2i2i000000000000000000000−2i2i0002+2i−2−2i2−2i−2+2i000000000000000000−1−i1+i−1+i1−i0000000000
χ744-44-4-24004i−4i2-22-44-4-202-2200004i−4i00−2i2i000000000000000000000−2i2i000−2−2i2+2i−2+2i2−2i0000000000000000001+i−1−i1−i−1+i0000000000
χ754-44-4-2400−4i4i2-22-44-4-202-220000−4i4i002i−2i0000000000000000000002i−2i0002−2i−2+2i2+2i−2−2i000000000000000000−1+i1−i−1−i1+i0000000000
χ764-44-4-2400−4i4i2-22-44-4-202-220000−4i4i002i−2i0000000000000000000002i−2i000−2+2i2−2i−2−2i2+2i0000000000000000001−i−1+i1+i−1−i0000000000
χ774-4-44444i−4i00-4-44-4-4440-4-44004i−4i004i−4i0000000000000000000004i−4i00000000000000000000000000000000000000000
χ784-4-4444−4i4i00-4-44-4-4440-4-4400−4i4i00−4i4i000000000000000000000−4i4i00000000000000000000000000000000000000000
χ794-4-444-24i−4i00-4-4422-2-2022-200−2i2i004i−4i0000000023−23−2323000000000−2i2i00000000000−2i32i30000000000000000000000000000
χ804-4-444-24i−4i00-4-4422-2-2022-200−2i2i004i−4i00000000−232323−23000000000−2i2i000000000002i3−2i30000000000000000000000000000
χ814-4-444-2−4i4i00-4-4422-2-2022-2002i−2i00−4i4i0000000023−23−23230000000002i−2i000000000002i3−2i30000000000000000000000000000
χ824-4-444-2−4i4i00-4-4422-2-2022-2002i−2i00−4i4i00000000−232323−230000000002i−2i00000000000−2i32i30000000000000000000000000000
χ834-4-44-244i−4i0022-2-4-44-2022-2004i−4i00−2i2i000000000000000000000−2i2i0000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000
χ844-4-44-244i−4i0022-2-4-44-2022-2004i−4i00−2i2i000000000000000000000−2i2i0000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000
χ854-4-44-24−4i4i0022-2-4-44-2022-200−4i4i002i−2i0000000000000000000002i−2i0000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000
χ864-4-44-24−4i4i0022-2-4-44-2022-200−4i4i002i−2i0000000000000000000002i−2i0000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000
χ8788-8-8-480000-4448-8-8-40-444000000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-444-444202-2-2−4i34i300000000000000000000000002i3−2i30000000000000000000000000000000000000000000
χ8988-8-8-4-40000-444-444202-2-24i3−4i30000000000000000000000000−2i32i30000000000000000000000000000000000000000000
χ908-88-8-4-4008i−8i4-444-4420-22-20000−4i4i00−4i4i0000000000000000000002i−2i000000000000000000000000000000000000000
χ918-88-8-4-400−8i8i4-444-4420-22-200004i−4i004i−4i000000000000000000000−2i2i000000000000000000000000000000000000000
χ928-8-88-4-48i−8i0044-444-420-2-2200−4i4i00−4i4i0000000000000000000002i−2i00000000000000000000000000000000000000000
χ938-8-88-4-4−8i8i0044-444-420-2-22004i−4i004i−4i000000000000000000000−2i2i00000000000000000000000000000000000000000

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