Finite Group Databasebeta

← Group #10827743

Character table — Group #10827743

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order1244222344461212224444446666666121212121212121212121222444466668888121212121212121212122424242424242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ6111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ911111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11-11-1-1-1111-11-1
χ1011111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-11-1111-1-1-11-11
χ1111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1-1-111-11-11
χ1211111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-11-11-1
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ172222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-21111-1-1-1-1-1-111111111000000000000
χ192222222-1222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111112222-2-2-1-1-1-1-2-2-2-2-1-1-1-111111111111111000000000000
χ202222222-1222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2-2-2111122221111111111-1-1-1-1-1-1-1-1000000000000
χ212222222-1222-1-1-1-2-2-2-22222-1-11111-1-1-1-11111-1-1-1-12-22-2-2-2-1-11122-2-2-1-111-1-11111-1-1-1-11111000000000000
χ222222222-1222-1-1-1-2-2-2-22222-1-11111-1-1-1-11111-1-1-1-1-22-22-2-211-1-1-2-22211-1-1-1-111111111-1-1-1-1000000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-1111111112-22-222-1-111-2-222-1-11111-1-1-1-11111-1-1-1-1000000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-1-111111111-22-222211-1-122-2-211-1-111-1-1-1-1-1-1-1-11111000000000000
χ252222-2-2222-2-22222-22-222-2-2-2-222-2-222-2-222-2-2222200002-2000000000000-2-222-2-200000000000000000000
χ262222-2-2222-2-22222-22-2-2-222-2-222-2-222-2-222-2-2-2-2-2-20000-2200000000000022-2-22200000000000000000000
χ272222-2-2222-2-2222-22-2222-2-2-2-2-2-22222-2-2-2-22222220000-22000000000000-2-2-2-22200000000000000000000
χ282222-2-2222-2-2222-22-22-2-222-2-2-2-22222-2-2-2-222-2-2-2-200002-20000000000002222-2-200000000000000000000
χ292222-2-22-12-2-2-1-1-12-22-222-2-211-1-111-1-111-1-111-1-1-1-100002-2−i3i3−i3i30000−i3i3−i3i311-1-111−i3−i3i3i3−i3−i3i3i3000000000000
χ302222-2-22-12-2-2-1-1-12-22-222-2-211-1-111-1-111-1-111-1-1-1-100002-2i3−i3i3−i30000i3−i3i3−i311-1-111i3i3−i3−i3i3i3−i3−i3000000000000
χ312222-2-22-12-2-2-1-1-12-22-2-2-22211-1-111-1-111-1-11111110000-22−i3i3−i3i30000−i3i3−i3i3-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ322222-2-22-12-2-2-1-1-12-22-2-2-22211-1-111-1-111-1-11111110000-22i3−i3i3−i30000i3−i3i3−i3-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ332222-2-22-12-2-2-1-1-1-22-2222-2-21111-1-1-1-11111-1-1-1-1-1-10000-22−i3i3i3−i30000−i3i3i3−i31111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ342222-2-22-12-2-2-1-1-1-22-2222-2-21111-1-1-1-11111-1-1-1-1-1-10000-22i3−i3−i3i30000i3−i3−i3i31111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ352222-2-22-12-2-2-1-1-1-22-22-2-2221111-1-1-1-11111-1-1111100002-2−i3i3i3−i30000−i3i3i3−i3-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000000000
χ362222-2-22-12-2-2-1-1-1-22-22-2-2221111-1-1-1-11111-1-1111100002-2i3−i3−i3i30000i3−i3−i3i3-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000000000
χ3722-2-22222-2-2-22-2-22-2-2200002222-2-22-2-2-2-2-22200000000000000000000000000000000000020-202-2000000
χ3822-2-22222-2-2-22-2-22-2-2200002222-2-22-2-2-2-2-222000000000000000000000000000000000000-2020-22000000
χ3922-2-22222-2-2-22-2-2-222-2000022-2-2222-2-2-222-2-200000000000000000000000000000000000020-20-22000000
χ4022-2-22222-2-2-22-2-2-222-2000022-2-2222-2-2-222-2-2000000000000000000000000000000000000-20202-2000000
χ4122-2-22-2-2222-22-2-200002i−2i2i−2i2-20000-222-200002i2i−2i−2i020-2000022002i−2i00-2-22i−2i000000002i−2i2i−2i000000000000
χ4222-2-22-2-2222-22-2-200002i−2i2i−2i2-20000-222-200002i2i−2i−2i0-2020000-2-200−2i2i00222i−2i00000000−2i2i−2i2i000000000000
χ4322-2-22-2-2222-22-2-20000−2i2i−2i2i2-20000-222-20000−2i−2i2i2i020-200002200−2i2i00-2-2−2i2i00000000−2i2i−2i2i000000000000
χ4422-2-22-2-2222-22-2-20000−2i2i−2i2i2-20000-222-20000−2i−2i2i2i0-2020000-2-2002i−2i0022−2i2i000000002i−2i2i−2i000000000000
χ4522-2-22-2-2-122-2-11100002i−2i2i−2i-11−i3i3−i3i31-1-11−i3i3−i3i3−i−iii020-200−i3i3-1-1002i−2ii3−i311−ii3−33−33−33−3−ii−ii000000000000
χ4622-2-22-2-2-122-2-11100002i−2i2i−2i-11−i3i3−i3i31-1-11−i3i3−i3i3−i−iii0-20200i3−i31100−2i2i−i3i3-1-1−ii3−33−3−33−33i−ii−i000000000000
χ4722-2-22-2-2-122-2-11100002i−2i2i−2i-11i3−i3i3−i31-1-11i3−i3i3−i3−i−iii020-200i3−i3-1-1002i−2i−i3i311−ii−33−33−33−33−ii−ii000000000000
χ4822-2-22-2-2-122-2-11100002i−2i2i−2i-11i3−i3i3−i31-1-11i3−i3i3−i3−i−iii0-20200−i3i31100−2i2ii3−i3-1-1−ii−33−333−33−3i−ii−i000000000000
χ4922-2-22-2-2-122-2-1110000−2i2i−2i2i-11−i3i3−i3i31-1-11−i3i3−i3i3ii−i−i020-200−i3i3-1-100−2i2ii3−i311i−i−33−33−33−33i−ii−i000000000000
χ5022-2-22-2-2-122-2-1110000−2i2i−2i2i-11−i3i3−i3i31-1-11−i3i3−i3i3ii−i−i0-20200i3−i311002i−2i−i3i3-1-1i−i−33−333−33−3−ii−ii000000000000
χ5122-2-22-2-2-122-2-1110000−2i2i−2i2i-11i3−i3i3−i31-1-11i3−i3i3−i3ii−i−i020-200i3−i3-1-100−2i2i−i3i311i−i3−33−33−33−3i−ii−i000000000000
χ5222-2-22-2-2-122-2-1110000−2i2i−2i2i-11i3−i3i3−i31-1-11i3−i3i3−i3ii−i−i0-20200−i3i311002i−2ii3−i3-1-1i−i3−33−3−33−33−ii−ii000000000000
χ5322-2-2-22-222-222-2-200002i−2i−2i2i-220000-22-2200002i2i−2i−2i20-200022002i−2i00-2-200−2i2i00002i−2i−2i2i0000000000000000
χ5422-2-2-22-222-222-2-200002i−2i−2i2i-220000-22-2200002i2i−2i−2i-202000-2-200−2i2i002200−2i2i0000−2i2i2i−2i0000000000000000
χ5522-2-2-22-222-222-2-20000−2i2i2i−2i-220000-22-220000−2i−2i2i2i20-20002200−2i2i00-2-2002i−2i0000−2i2i2i−2i0000000000000000
χ5622-2-2-22-222-222-2-20000−2i2i2i−2i-220000-22-220000−2i−2i2i2i-202000-2-2002i−2i0022002i−2i00002i−2i−2i2i0000000000000000
χ5722-2-2-22-2-12-22-11100002i−2i−2i2i1-1−i3i3i3−i31-11-1−i3i3i3−i3−i−iii20-2000-1-1−i3i32i−2i0011i3−i3i−i3−3−33−iii−i3−3−33000000000000
χ5822-2-2-22-2-12-22-11100002i−2i−2i2i1-1−i3i3i3−i31-11-1−i3i3i3−i3−i−iii-20200011i3−i3−2i2i00-1-1−i3i3i−i3−3−33i−i−ii−333−3000000000000
χ5922-2-2-22-2-12-22-11100002i−2i−2i2i1-1i3−i3−i3i31-11-1i3−i3−i3i3−i−iii20-2000-1-1i3−i32i−2i0011−i3i3i−i−333−3−iii−i−333−3000000000000
χ6022-2-2-22-2-12-22-11100002i−2i−2i2i1-1i3−i3−i3i31-11-1i3−i3−i3i3−i−iii-20200011−i3i3−2i2i00-1-1i3−i3i−i−333−3i−i−ii3−3−33000000000000
χ6122-2-2-22-2-12-22-1110000−2i2i2i−2i1-1−i3i3i3−i31-11-1−i3i3i3−i3ii−i−i20-2000-1-1−i3i3−2i2i0011i3−i3−ii−333−3i−i−ii−333−3000000000000
χ6222-2-2-22-2-12-22-1110000−2i2i2i−2i1-1−i3i3i3−i31-11-1−i3i3i3−i3ii−i−i-20200011i3−i32i−2i00-1-1−i3i3−ii−333−3−iii−i3−3−33000000000000
χ6322-2-2-22-2-12-22-1110000−2i2i2i−2i1-1i3−i3−i3i31-11-1i3−i3−i3i3ii−i−i20-2000-1-1i3−i3−2i2i0011−i3i3−ii3−3−33i−i−ii3−3−33000000000000
χ6422-2-2-22-2-12-22-1110000−2i2i2i−2i1-1i3−i3−i3i31-11-1i3−i3−i3i3ii−i−i-20200011−i3i32i−2i00-1-1i3−i3−ii3−3−33−iii−i−333−3000000000000
χ6522-2-2-2-222-2222-2-222-2-20000-2-222222-222-2-2-2-2000000000000000000000000000000000000020-2002-20000
χ6622-2-2-2-222-2222-2-222-2-20000-2-222222-222-2-2-2-20000000000000000000000000000000000000-20200-220000
χ6722-2-2-2-222-2222-2-2-2-2220000-2-2-2-2-2-22-2222222000000000000000000000000000000000000020-200-220000
χ6822-2-2-2-222-2222-2-2-2-2220000-2-2-2-2-2-22-22222220000000000000000000000000000000000000-202002-20000
χ6944444-4-44-4-44444000000004-40000-4-4-440000000000000000000000000000000000000000000000000000
χ7044444-4-4-2-4-44-2-2-200000000-22−2i32i32i3−2i3222-22i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ7144444-4-4-2-4-44-2-2-200000000-222i3−2i3−2i32i3222-2−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ724444-44-44-44-444400000000-440000-4-44-40000000000000000000000000000000000000000000000000000
χ734444-44-4-2-44-4-2-2-2000000002-2−2i32i3−2i32i322-222i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ744444-44-4-2-44-4-2-2-2000000002-22i3−2i32i3−2i322-22−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2224-4-440000-2-2-2-222-222222-2-2000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-222-444-40000-2-222-2-2-2222-2-222000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-444-22244-4-4000022-2-2-2-2-22-2-22222000000000000000000000000000000000000000000000000
χ7844-4-4-4-44-2-444-222-4-4440000222222-22-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ798-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-40004−4i4i0000000000000000000000−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ1100000000000000000000000000000000000000000000
χ818-88i−8i000-40004−4i4i00000000000000000000002ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ1100000000000000000000000000000000000000000000
χ828-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-400044i−4i0000000000000000000000−2ζ2+2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10−2ζ1100000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i−4i00000000000000000000002ζ2−2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10+2ζ1100000000000000000000000000000000000000000000

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