Finite Group Databasebeta

← Group #10897673

Character table — Group #10897673

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222244444444888888888888888888881212121216161616161616161616242424242424242424244848
order1244222344466612121212444466121224888888121212122424242424242424888846812121224242424224444888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-11-1-1111-11-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-11-1111-1-1-1-111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1111-111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111-111-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-1-1-11111-1-11-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-11111-1-1-1-111-11
χ11111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1-11-11-1-111-1-1-11
χ12111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-1-1-11-11-111-1-1111-1
χ13111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1111-11-111-1-1-1-1-11
χ14111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-111-11-11-1-111111-1
χ15111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-111111111-1-1-1-1-1-11-1
χ16111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-11111-1-1-1-1111111-11
χ172222222-1222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-1-1-1-12222-2-2-2-2-1-1-1-1111111110000-2-1-211-111-1-1000000000000
χ192222222-1222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000-21-21111111000000000000
χ202222222-1222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000212-1-11-1-111000000000000
χ212222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-222-2-21111-1-1-1-111110000-2-1211-1-1-111000000000000
χ222222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-2-22211111111-1-1-1-100002-1-2-1-1-11111000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22222-2-21111-1-1-1-11111000021-2-1-1111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-10000-212111-1-1-1-1000000000000
χ252222-2-222-2-22-2-22-2-22222-2-2-22-220000000022-2-20000000022-2-20000000000000000002-200
χ262222-2-222-2-22-2-22-2-22222-2-2-22-220000000022-2-200000000-2-222000000000000000000-2200
χ272222-2-222-2-22-2-22-2-222-2-222-22-2200000000-2-2220000000022-2-2000000000000000000-2200
χ282222-2-222-2-22-2-22-2-222-2-222-22-2200000000-2-22200000000-2-2220000000000000000002-200
χ2922-2-22222-2-2-2222-2-2-2-2000022-2-200002i−2i0000002i2i−2i−2i00002i−2i2i−2i000000000000002-2000000
χ3022-2-22222-2-2-2222-2-2-2-2000022-2-200002i−2i0000002i2i−2i−2i0000−2i2i−2i2i00000000000000-22000000
χ3122-2-22222-2-2-2222-2-2-2-2000022-2-20000−2i2i000000−2i−2i2i2i00002i−2i2i−2i00000000000000-22000000
χ3222-2-22222-2-2-2222-2-2-2-2000022-2-20000−2i2i000000−2i−2i2i2i0000−2i2i−2i2i000000000000002-2000000
χ3322-2-22-2-22-222222-2-2-2-22i−2i2i−2i-2-2222-22i−2i00002i−2i2i−2i00000000000002000-2002i−2i000000000000
χ3422-2-22-2-22-222222-2-2-2-22i−2i2i−2i-2-222-22−2i2i00002i−2i2i−2i0000000000000-2000200−2i2i000000000000
χ3522-2-22-2-22-222222-2-2-2-2−2i2i−2i2i-2-2222-2−2i2i0000−2i2i−2i2i00000000000002000-200−2i2i000000000000
χ3622-2-22-2-22-222222-2-2-2-2−2i2i−2i2i-2-222-222i−2i0000−2i2i−2i2i0000000000000-20002002i−2i000000000000
χ3722-2-22-2-2-1-222-1-1-111112i−2i2i−2i11-1-12-22i−2i0000−ii−ii3−33−3−i3−i3i3i300000-10−i3i313−3−ii000000000000
χ3822-2-22-2-2-1-222-1-1-111112i−2i2i−2i11-1-12-22i−2i0000−ii−ii−33−33i3i3−i3−i300000-10i3−i31−33−ii000000000000
χ3922-2-22-2-2-1-222-1-1-111112i−2i2i−2i11-1-1-22−2i2i0000−ii−ii3−33−3−i3−i3i3i30000010i3−i3-1−33i−i000000000000
χ4022-2-22-2-2-1-222-1-1-111112i−2i2i−2i11-1-1-22−2i2i0000−ii−ii−33−33i3i3−i3−i30000010−i3i3-13−3i−i000000000000
χ4122-2-22-2-2-1-222-1-1-11111−2i2i−2i2i11-1-12-2−2i2i0000i−ii−i3−33−3i3i3−i3−i300000-10i3−i313−3i−i000000000000
χ4222-2-22-2-2-1-222-1-1-11111−2i2i−2i2i11-1-12-2−2i2i0000i−ii−i−33−33−i3−i3i3i300000-10−i3i31−33i−i000000000000
χ4322-2-22-2-2-1-222-1-1-11111−2i2i−2i2i11-1-1-222i−2i0000i−ii−i3−33−3i3i3−i3−i30000010−i3i3-1−33−ii000000000000
χ4422-2-22-2-2-1-222-1-1-11111−2i2i−2i2i11-1-1-222i−2i0000i−ii−i−33−33−i3−i3i3i30000010i3−i3-13−3−ii000000000000
χ4522-2-2-22-222-22-2-2222-2-22i−2i−2i2i2-2-22000000002i−2i−2i2i000000000000000000000020-20002i−2i0000
χ4622-2-2-22-222-22-2-2222-2-22i−2i−2i2i2-2-22000000002i−2i−2i2i0000000000000000000000-202000−2i2i0000
χ4722-2-2-22-222-22-2-2222-2-2−2i2i2i−2i2-2-2200000000−2i2i2i−2i000000000000000000000020-2000−2i2i0000
χ4822-2-2-22-222-22-2-2222-2-2−2i2i2i−2i2-2-2200000000−2i2i2i−2i0000000000000000000000-2020002i−2i0000
χ4922-2-2-2-22222-2-2-2222-2-20000-222-20000002i−2i000000002i−2i2i−2i2i−2i−2i2i0000000000020-200000000
χ5022-2-2-2-22222-2-2-2222-2-20000-222-20000002i−2i000000002i−2i2i−2i−2i2i2i−2i00000000000-20200000000
χ5122-2-2-2-22222-2-2-2222-2-20000-222-2000000−2i2i00000000−2i2i−2i2i2i−2i−2i2i00000000000-20200000000
χ5222-2-2-2-22222-2-2-2222-2-20000-222-2000000−2i2i00000000−2i2i−2i2i−2i2i2i−2i0000000000020-200000000
χ5344444-4-444-4-444444440000-4-4-4-40000000000000000000000000000000000000000000000
χ5444444-4-4-24-4-4-2-2-2-2-2-2-200002222000000000000−2i32i32i3−2i3000000000000000000000000000000
χ5544444-4-4-24-4-4-2-2-2-2-2-2-2000022220000000000002i3−2i3−2i32i3000000000000000000000000000000
χ564444-44-44-44-4-4-44-4-44400004-44-40000000000000000000000000000000000000000000000
χ574444-44-4-2-44-422-222-2-20000-22-22000000000000000023−23−232300000000000000000000000000
χ584444-44-4-2-44-422-222-2-20000-22-220000000000000000−232323−2300000000000000000000000000
χ594444-4-44-2-4-4422-222-2-244-4-42-22-200000000-2-2220000000000000000000000000000000000
χ604444-4-44-2-4-4422-222-2-2-4-4442-22-20000000022-2-20000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2-2-222220000-2-22200004i−4i000000−2i−2i2i2i000000000000000000000000000000
χ6244-4-4444-2-4-4-4-2-2-222220000-2-2220000−4i4i0000002i2i−2i−2i000000000000000000000000000000
χ6344-4-4-44-4-24-4422-2-2-2224i−4i−4i4i-222-200000000−2i2i2i−2i0000000000000000000000000000000000
χ6444-4-4-44-4-24-4422-2-2-222−4i4i4i−4i-222-2000000002i−2i−2i2i0000000000000000000000000000000000
χ6544-4-4-4-44-244-422-2-2-22200002-2-220000004i−4i00000000−2i2i−2i2i00000000000000000000000000
χ6644-4-4-4-44-244-422-2-2-22200002-2-22000000−4i4i000000002i−2i2i−2i00000000000000000000000000
χ678-88i−8i000800000-8008i−8i000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-4000−4i34i3443−43−4i4i000000000000000000000000000000000000000000000000000000
χ698-88i−8i000-40004i3−4i34−4343−4i4i000000000000000000000000000000000000000000000000000000
χ708-8−8i8i000800000-800−8i8i000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-4000−4i34i34−43434i−4i000000000000000000000000000000000000000000000000000000
χ728-8−8i8i000-40004i3−4i3443−434i−4i000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).