Finite Group Databasebeta

← Group #10827741

Character table — Group #10827741

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222244444444888888888888888888881212121216161616161616161616242424242424242424244848
order12442223444666121212124444661212224444668812121212121212121212224446812121224242424224444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-11-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1
χ4111111111111111111111111111-11-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111
χ511111111111111111111111111-11-11-1-1-1-111-1-11111-1-1-1-11111-11-1-1-1111-1-1-11-1111-1-111-1-1
χ611111111111111111111111111-11-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1111-1-11-11-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-111-1-1-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-1-1111111-1-11111-1-1
χ9111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1111-1-1-1-1-11-11-1-111-1-11-1
χ10111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11-11-111-1-111-11
χ11111111111111111111-1-1-1-111111-11-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-11111-1-1-1-1-1-11111-11
χ12111111111111111111-1-1-1-111111-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1-1-1-11-1
χ13111111111111111111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-111111111-111-1-11-1-1111111-1-1-1-1-1-1-11
χ14111111111111111111-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-1-1-11111111-1
χ15111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1111111111-1-111-111-1-11-11-1-1-1-1-1111-1
χ16111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-1-111-111-1-1-11-111111-1-1-11
χ172222222-1222-1-1-1-1-1-1-12222-1-1-1-1222222-1-122-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-1-1-1-12-22-222-1-1-2-2-1-1-1-1-1-1-1-1-1-10000-21-21111111000000000000
χ192222222-1222-1-1-1-1-1-1-12222-1-1-1-1-22-22-2-2112211-1-1-1-111110000-2-1-211-1-1-111000000000000
χ202222222-1222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-211-2-211-1-1-1-111110000212-1-1111-1-1000000000000
χ212222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-2-2-1-1-2-2-1-11111111100002-1-2-1-1-11111000000000000
χ222222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-22-2-2-2-1-122-1-1111111110000-212111-1-1-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-22-222211-2-2111111-1-1-1-10000-2-1211-111-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2221122111111-1-1-1-1000021-2-1-11-1-111000000000000
χ252222-2-2222-2-2-2-2222-2-222-2-2-222-200000000000022-2-200002-22-2000000000000002-2000000
χ262222-2-2222-2-2-2-2222-2-222-2-2-222-200000000000022-2-20000-22-2200000000000000-22000000
χ272222-2-2222-2-2-2-2222-2-2-2-222-222-2000000000000-2-22200002-22-200000000000000-22000000
χ282222-2-2222-2-2-2-2222-2-2-2-222-222-2000000000000-2-2220000-22-22000000000000002-2000000
χ2922-2-22222-2-2-2222-2-2-2-2000022-2-220-20002200-2-2000000002-2-2200000000000000002-20000
χ3022-2-22222-2-2-2222-2-2-2-2000022-2-220-20002200-2-200000000-222-20000000000000000-220000
χ3122-2-22222-2-2-2222-2-2-2-2000022-2-2-202000-2-20022000000002-2-220000000000000000-220000
χ3222-2-22222-2-2-2222-2-2-2-2000022-2-2-202000-2-2002200000000-222-200000000000000002-20000
χ3322-2-22-2-222-22222-2-2-2-22i−2i2i−2i-2-222020-200002i−2i002i−2i2i−2i0000000002000-22i−2i00000000000000
χ3422-2-22-2-222-22222-2-2-2-22i−2i2i−2i-2-2220-2020000−2i2i002i−2i2i−2i000000000-20002−2i2i00000000000000
χ3522-2-22-2-222-22222-2-2-2-2−2i2i−2i2i-2-222020-20000−2i2i00−2i2i−2i2i0000000002000-2−2i2i00000000000000
χ3622-2-22-2-222-22222-2-2-2-2−2i2i−2i2i-2-2220-20200002i−2i00−2i2i−2i2i000000000-200022i−2i00000000000000
χ3722-2-22-2-2-12-22-1-1-111112i−2i2i−2i11-1-1020-200−i3i32i−2i−i3i3−ii−ii33−3−300000-10−i3i31−ii3−3000000000000
χ3822-2-22-2-2-12-22-1-1-111112i−2i2i−2i11-1-1020-200i3−i32i−2ii3−i3−ii−ii−3−33300000-10i3−i31−ii−33000000000000
χ3922-2-22-2-2-12-22-1-1-111112i−2i2i−2i11-1-10-20200−i3i3−2i2i−i3i3−ii−ii33−3−30000010i3−i3-1i−i−33000000000000
χ4022-2-22-2-2-12-22-1-1-111112i−2i2i−2i11-1-10-20200i3−i3−2i2ii3−i3−ii−ii−3−3330000010−i3i3-1i−i3−3000000000000
χ4122-2-22-2-2-12-22-1-1-11111−2i2i−2i2i11-1-1020-200−i3i3−2i2i−i3i3i−ii−i−3−33300000-10−i3i31i−i−33000000000000
χ4222-2-22-2-2-12-22-1-1-11111−2i2i−2i2i11-1-1020-200i3−i3−2i2ii3−i3i−ii−i33−3−300000-10i3−i31i−i3−3000000000000
χ4322-2-22-2-2-12-22-1-1-11111−2i2i−2i2i11-1-10-20200−i3i32i−2i−i3i3i−ii−i−3−3330000010i3−i3-1−ii3−3000000000000
χ4422-2-22-2-2-12-22-1-1-11111−2i2i−2i2i11-1-10-20200i3−i32i−2ii3−i3i−ii−i33−3−30000010−i3i3-1−ii−33000000000000
χ4522-2-2-22-2222-2-2-22-2-2222i−2i−2i2i2-22-20000000000002i−2i−2i2i000000000000000000020-200002i−2i00
χ4622-2-2-22-2222-2-2-22-2-2222i−2i−2i2i2-22-20000000000002i−2i−2i2i0000000000000000000-2020000−2i2i00
χ4722-2-2-22-2222-2-2-22-2-222−2i2i2i−2i2-22-2000000000000−2i2i2i−2i000000000000000000020-20000−2i2i00
χ4822-2-2-22-2222-2-2-22-2-222−2i2i2i−2i2-22-2000000000000−2i2i2i−2i0000000000000000000-20200002i−2i00
χ4922-2-2-2-222-222-2-22-2-2220000-22-2200002-200000000002-22-222-2-2000000000020-2000000000
χ5022-2-2-2-222-222-2-22-2-2220000-22-2200002-200000000002-22-2-2-2220000000000-202000000000
χ5122-2-2-2-222-222-2-22-2-2220000-22-220000-220000000000-22-2222-2-20000000000-202000000000
χ5222-2-2-2-222-222-2-22-2-2220000-22-220000-220000000000-22-22-2-222000000000020-2000000000
χ5344444-4-44-44-444444440000-4-4-4-40000000000000000000000000000000000000000000000
χ5444444-4-4-2-44-4-2-2-2-2-2-2-200002222000000−2i32i3002i3−2i30000000000000000000000000000000000
χ5544444-4-4-2-44-4-2-2-2-2-2-2-2000022220000002i3−2i300−2i32i30000000000000000000000000000000000
χ564444-44-44-4-44-4-4444-4-400004-4-440000000000000000000000000000000000000000000000
χ574444-44-4-2-4-4422-2-2-2220000-222-2000000000000000023−23−232300000000000000000000000000
χ584444-44-4-2-4-4422-2-2-2220000-222-20000000000000000−232323−2300000000000000000000000000
χ594444-4-44-24-4-422-2-2-22244-4-42-2-22000000000000-2-222000000000000000000000000000000
χ604444-4-44-24-4-422-2-2-222-4-4442-2-2200000000000022-2-2000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2-2-222220000-2-22240-4000-2-200220000000000000000000000000000000000
χ6244-4-4444-2-4-4-4-2-2-222220000-2-222-4040002200-2-20000000000000000000000000000000000
χ6344-4-4-44-4-244-422-222-2-24i−4i−4i4i-22-22000000000000−2i2i2i−2i000000000000000000000000000000
χ6444-4-4-44-4-244-422-222-2-2−4i4i4i−4i-22-220000000000002i−2i−2i2i000000000000000000000000000000
χ6544-4-4-4-44-2-44422-222-2-200002-22-200004-40000000000-22-2200000000000000000000000000
χ6644-4-4-4-44-2-44422-222-2-200002-22-20000-4400000000002-22-200000000000000000000000000
χ678-88i−8i000800000-88i−8i00000000000000000000000000000000000000000000000000000000
χ688-88i−8i000-4000−4i34i34−4i4i43−43000000000000000000000000000000000000000000000000000000
χ698-88i−8i000-40004i3−4i34−4i4i−4343000000000000000000000000000000000000000000000000000000
χ708-8−8i8i000800000-8−8i8i00000000000000000000000000000000000000000000000000000000
χ718-8−8i8i000-4000−4i34i344i−4i−4343000000000000000000000000000000000000000000000000000000
χ728-8−8i8i000-40004i3−4i344i−4i43−43000000000000000000000000000000000000000000000000000000

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