Finite Group Databasebeta

← Group #10690981

Character table — Group #10690981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12223444444446661212121224466888812121212121244448812121212121212121212242424242424242422448824242424448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111-1-111-1-1-1-11111111-111-1-1ii−i−i-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-11-1ii−i−iii−i−i1-1
χ1011111-1-111-1-1-1-11111111-111-1-1ii−i−i-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-1-11−i−iii−i−iii-11
χ1111111-1-111-1-1-1-11111111-111-1-1ii−i−i-1-1-1-1-1-1−i−iiii−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-1111-1−i−iiiii−i−i-11
χ1211111-1-111-1-1-1-11111111-111-1-1ii−i−i-1-1-1-1-1-1−i−iiii−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111-11ii−i−i−i−iii1-1
χ1311111-1-111-1-1-1-11111111-111-1-1−i−iii-1-1-1-1-1-1ii−i−i−ii11iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-1111-1ii−i−i−i−iii-11
χ1411111-1-111-1-1-1-11111111-111-1-1−i−iii-1-1-1-1-1-1ii−i−i−ii11iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111-11−i−iiiii−i−i1-1
χ1511111-1-111-1-1-1-11111111-111-1-1−i−iii-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-11-1−i−iii−i−iii1-1
χ1611111-1-111-1-1-1-11111111-111-1-1−i−iii-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-1-11ii−i−iii−i−i-11
χ17222222222-2-2222222222-2-2-2-2-2000022-2-222000000-2-200000000000000002222000000-2-20000000000
χ18222222222-2-2222222222-2-2-2-2-2000022-2-222000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222-2-222-2-2222-2-2-2-2-2-22-2-200002222-2-20000002-2000000000000000000000000000000002i−2i2i−2i00
χ202222222-2-222-2-2222-2-2-2-2-2-22-2-200002222-2-20000002-200000000000000000000000000000000−2i2i−2i2i00
χ212222222-2-2-2-2-2-2222-2-2-2-222-2222i2i−2i−2i22-2-2-2-20000−2i2i-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-222-222−2i−2i2i2i22-2-2-2-200002i−2i-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ2322222-2-22222-2-222222222-2-2220000-2-222-2-2000000-2-2000000000000000022-2-2000000-220000000000
χ2422222-2-22222-2-222222222-2-2220000-2-222-2-2000000-2-20000000000000000-2-2220000002-20000000000
χ2522222-2-2-2-22222222-2-2-2-2-22-2-2-22222-2-222220000-2-2-220000000022-2-2-2-2220000000000000000000000
χ2622222-2-2-2-22222222-2-2-2-2-22-2-2-2-2-2-2-2-2-22222000022-2200000000-2-22222-2-20000000000000000000000
χ2722222-2-2-2-2-2-222222-2-2-2-22-22220000-2-2-2-2220000002-2000000000000000000000000000000002-2-2200
χ2822222-2-2-2-2-2-222222-2-2-2-22-22220000-2-2-2-2220000002-200000000000000000000000000000000-222-200
χ292222-122222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ332222-122-2-2-2-2-2-2-1-1-1111122-2-1-12i2i−2i−2i-1-111110000−2i2i1-1−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000003−33−3000000000000
χ342222-122-2-2-2-2-2-2-1-1-1111122-2-1-12i2i−2i−2i-1-111110000−2i2i1-1i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii000000−33−33000000000000
χ352222-122-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i2i2i-1-1111100002i−2i1-1−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i000000−33−33000000000000
χ362222-122-2-2-2-2-2-2-1-1-1111122-2-1-1−2i−2i2i2i-1-1111100002i−2i1-1i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000003−33−3000000000000
χ372222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-222112i2i−2i−2i1111112i2i−2i−2i2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ382222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-222112i2i−2i−2i111111−2i−2i2i2i2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ392222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22211−2i−2i2i2i1111112i2i−2i−2i−2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ402222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22211−2i−2i2i2i111111−2i−2i2i2i−2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ412222-1-2-2-2-22222-1-1-11111-22-211222211-1-1-1-10000-2-21-133−3−3−3−333-1-11111-1-1000000−333−3000000000000
χ422222-1-2-2-2-22222-1-1-11111-22-211222211-1-1-1-10000-2-21-1−3−33333−3−3-1-11111-1-10000003−3−33000000000000
χ432222-1-2-2-2-22222-1-1-11111-22-211-2-2-2-211-1-1-1-10000221-133−3−3−3−33311-1-1-1-1110000003−3−33000000000000
χ442222-1-2-2-2-22222-1-1-11111-22-211-2-2-2-211-1-1-1-10000221-1−3−33333−3−311-1-1-1-111000000−333−3000000000000
χ452-22-222i−2i2-2002i−2i2-2-222-2-20000000002i−2i002i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-22i−2i000000001+i−1−i1−i−1+i000000
χ462-22-222i−2i2-2002i−2i2-2-222-2-20000000002i−2i002i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000-22−2i2i00000000−1−i1+i−1+i1−i000000
χ472-22-222i−2i2-2002i−2i2-2-222-2-20000000002i−2i002i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-22i−2i00000000−1−i1+i−1+i1−i000000
χ482-22-222i−2i2-2002i−2i2-2-222-2-20000000002i−2i002i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000-22−2i2i000000001+i−1−i1−i−1+i000000
χ492-22-22−2i2i2-200−2i2i2-2-222-2-2000000000−2i2i00−2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002-2−2i2i000000001−i−1+i1+i−1−i000000
χ502-22-22−2i2i2-200−2i2i2-2-222-2-2000000000−2i2i00−2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000-222i−2i00000000−1+i1−i−1−i1+i000000
χ512-22-22−2i2i2-200−2i2i2-2-222-2-2000000000−2i2i00−2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002-2−2i2i00000000−1+i1−i−1−i1+i000000
χ522-22-22−2i2i2-200−2i2i2-2-222-2-2000000000−2i2i00−2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000-222i−2i000000001−i−1+i1+i−1−i000000
χ534444-24444-4-444-2-2-2-2-2-2-2-4-4-4220000-2-222-2-20000002200000000000000000000000000000000000000
χ544444-244-4-444-4-4-2-2-22222-4-44220000-2-2-2-222000000-2200000000000000000000000000000000000000
χ554444-2-4-44444-4-4-2-2-2-2-2-2-24-4-4-2-2000022-2-2220000002200000000000000000000000000000000000000
χ564444-2-4-4-4-4-4-444-2-2-222224-44-2-200002222-2-2000000-2200000000000000000000000000000000000000
χ574-44-444i−4i-4400−4i4i4-4-4-4-4440000000004i−4i00−4i4i0000000000000000000000000000000000000000000000
χ584-44-44−4i4i-44004i−4i4-4-4-4-444000000000−4i4i004i−4i0000000000000000000000000000000000000000000000
χ594-44-4-24i−4i4-4004i−4i-222-2-222000000000−2i2i00−2i2i2+2i−2−2i2−2i−2+2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000000000
χ604-44-4-24i−4i4-4004i−4i-222-2-222000000000−2i2i00−2i2i−2−2i2+2i−2+2i2−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000000000
χ614-44-4-24i−4i-4400−4i4i-22222-2-2000000000−2i2i002i−2i00000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000000000
χ624-44-4-24i−4i-4400−4i4i-22222-2-2000000000−2i2i002i−2i00000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000000000
χ634-44-4-2−4i4i4-400−4i4i-222-2-2220000000002i−2i002i−2i2−2i−2+2i2+2i−2−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000000000
χ644-44-4-2−4i4i4-400−4i4i-222-2-2220000000002i−2i002i−2i−2+2i2−2i−2−2i2+2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000000000
χ654-44-4-2−4i4i-44004i−4i-22222-2-20000000002i−2i00−2i2i00000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000000000
χ664-44-4-2−4i4i-44004i−4i-22222-2-20000000002i−2i00−2i2i00000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000000000
χ674-4-44400004i−4i00-44-40000000002+2i−2−2i2−2i−2+2i004i−4i0000000000000000002+2i−2−2i00002−2i−2+2i0000000000000000000000
χ684-4-44400004i−4i00-44-4000000000−2−2i2+2i−2+2i2−2i004i−4i000000000000000000−2−2i2+2i0000−2+2i2−2i0000000000000000000000
χ694-4-4440000−4i4i00-44-40000000002−2i−2+2i2+2i−2−2i00−4i4i0000000000000000002−2i−2+2i00002+2i−2−2i0000000000000000000000
χ704-4-4440000−4i4i00-44-4000000000−2+2i2−2i−2−2i2+2i00−4i4i000000000000000000−2+2i2−2i0000−2−2i2+2i0000000000000000000000
χ714-4-44-200004i−4i002-2223−2323−23000−2i32i32+2i−2−2i2−2i−2+2i00−2i2i000000000000000000−1−i1+i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−1+i1−i0000000000000000000000
χ724-4-44-200004i−4i002-2223−2323−23000−2i32i3−2−2i2+2i−2+2i2−2i00−2i2i0000000000000000001+i−1−iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ111−i−1+i0000000000000000000000
χ734-4-44-200004i−4i002-22−2323−23230002i3−2i32+2i−2−2i2−2i−2+2i00−2i2i000000000000000000−1−i1+iζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−1+i1−i0000000000000000000000
χ744-4-44-200004i−4i002-22−2323−23230002i3−2i3−2−2i2+2i−2+2i2−2i00−2i2i0000000000000000001+i−1−i−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ111−i−1+i0000000000000000000000
χ754-4-44-20000−4i4i002-2223−2323−230002i3−2i32−2i−2+2i2+2i−2−2i002i−2i000000000000000000−1+i1−iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−1−i1+i0000000000000000000000
χ764-4-44-20000−4i4i002-2223−2323−230002i3−2i3−2+2i2−2i−2−2i2+2i002i−2i0000000000000000001−i−1+i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ111+i−1−i0000000000000000000000
χ774-4-44-20000−4i4i002-22−2323−2323000−2i32i32−2i−2+2i2+2i−2−2i002i−2i000000000000000000−1+i1−i−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−1−i1+i0000000000000000000000
χ784-4-44-20000−4i4i002-22−2323−2323000−2i32i3−2+2i2−2i−2−2i2+2i002i−2i0000000000000000001−i−1+iζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ111+i−1−i0000000000000000000000
χ7988-8-8800000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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