Finite Group Databasebeta

← Group #10707209

Character table — Group #10707209

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222344444466688881212121212122424242416161616242448484848484848482466881212242424248888161616162488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ91111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-111i−i-1-1ii−i−ii−ii−i11-1-11-1i−i
χ101111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-111i−i-1-1ii−i−i−ii−ii-1-111-11−ii
χ111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11-1-1−ii11−i−iiii−ii−i11-1-1-11−ii
χ121111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11-1-1−ii11−i−iii−ii−ii-1-1111-1i−i
χ131111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-111−ii-1-1−i−iiii−ii−i-1-111-11i−i
χ141111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-111−ii-1-1−i−iii−ii−ii11-1-11-1−ii
χ151111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11-1-1i−i11ii−i−ii−ii−i-1-1111-1−ii
χ161111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11-1-1i−i11ii−i−i−ii−ii11-1-1-11i−i
χ1722222222222222-2-2-2-2222222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ1822222222222222-2-2-2-2222222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ192222222-2-2-2-222222-2-2-2-222-2-222220000-2-2000000000000000000002i−2i−2i2i00000000
χ202222222-2-2-2-222222-2-2-2-222-2-222220000-2-200000000000000000000−2i2i2i−2i00000000
χ212222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ222222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-11111000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-1000000000000
χ252222-122-2-2-2-2-1-1-1-2-22211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii2-2-1-12i−2i11−i−iii000000000000
χ262222-122-2-2-2-2-1-1-1-2-22211-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii-2211−2i2i-1-1ii−i−i000000000000
χ272222-122-2-2-2-2-1-1-1-2-22211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i000000000000
χ282222-122-2-2-2-2-1-1-1-2-22211-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i-22112i−2i-1-1−i−iii000000000000
χ2922-2-222-22i−2i2i−2i2-2-22i−2i2-22i−2i2-22i−2i2i2i−2i−2i00002-20000000000000000000000002-22i−2i0000
χ3022-2-222-22i−2i2i−2i2-2-22i−2i2-22i−2i2-22i−2i2i2i−2i−2i00002-2000000000000000000000000-22−2i2i0000
χ3122-2-222-22i−2i2i−2i2-2-2−2i2i-222i−2i2-22i−2i−2i−2i2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-22−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ3222-2-222-22i−2i2i−2i2-2-2−2i2i-222i−2i2-22i−2i−2i−2i2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ3322-2-222-2−2i2i−2i2i2-2-22i−2i-22−2i2i2-2−2i2i2i2i−2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ3422-2-222-2−2i2i−2i2i2-2-22i−2i-22−2i2i2-2−2i2i2i2i−2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ3522-2-222-2−2i2i−2i2i2-2-2−2i2i2-2−2i2i2-2−2i2i−2i−2i2i2i00002-20000000000000000000000002-2−2i2i0000
χ3622-2-222-2−2i2i−2i2i2-2-2−2i2i2-2−2i2i2-2−2i2i−2i−2i2i2i00002-2000000000000000000000000-222i−2i0000
χ3722-2-2-12-22i−2i2i−2i-111−2i2i-22−ii-11−iiii−i−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300−i3i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ3822-2-2-12-22i−2i2i−2i-111−2i2i-22−ii-11−iiii−i−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300i3−i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ3922-2-2-12-22i−2i2i−2i-111−2i2i-22−ii-11−iiii−i−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300−i3i3003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ4022-2-2-12-22i−2i2i−2i-111−2i2i-22−ii-11−iiii−i−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300i3−i300−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ4122-2-2-12-2−2i2i−2i2i-1112i−2i-22i−i-11i−i−i−iii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300−i3i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ4222-2-2-12-2−2i2i−2i2i-1112i−2i-22i−i-11i−i−i−iii2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300i3−i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ4322-2-2-12-2−2i2i−2i2i-1112i−2i-22i−i-11i−i−i−iii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300−i3i300−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ4422-2-2-12-2−2i2i−2i2i-1112i−2i-22i−i-11i−i−i−iii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300i3−i3003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ4544444-4-444-4-44440000-4-4-4-444000000000000000000000000000000000000000000
χ4644444-4-4-4-444444000044-4-4-4-4000000000000000000000000000000000000000000
χ474444-2444444-2-2-2-4-4-4-4-2-2-2-2-2-2222200002200000000000000000000000000000000
χ484444-244-4-4-4-4-2-2-244-4-422-2-222-2-2-2-200002200000000000000000000000000000000
χ494444-2-4-444-4-4-2-2-200002222-2-20000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ504444-2-4-444-4-4-2-2-200002222-2-20000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ514444-2-4-4-4-444-2-2-20000-2-2222200000000006−66−6−66−66000000000000000000000000
χ524444-2-4-4-4-444-2-2-20000-2-222220000000000−66−666−66−6000000000000000000000000
χ5344-4-44-444i−4i−4i4i4-4-40000−4i4i-444i−4i000000000000000000000000000000000000000000
χ5444-4-44-44−4i4i4i−4i4-4-400004i−4i-44−4i4i000000000000000000000000000000000000000000
χ5544-4-4-24-44i−4i4i−4i-2224i−4i4-4−2i2i-22−2i2i−2i−2i2i2i0000-2200000000000000000000000000000000
χ5644-4-4-24-4−4i4i−4i4i-222−4i4i4-42i−2i-222i−2i2i2i−2i−2i0000-2200000000000000000000000000000000
χ5744-4-4-2-444i−4i−4i4i-22200002i−2i2-2−2i2i0000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000
χ5844-4-4-2-444i−4i−4i4i-22200002i−2i2-2−2i2i0000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ5944-4-4-2-44−4i4i4i−4i-2220000−2i2i2-22i−2i0000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ6044-4-4-2-44−4i4i4i−4i-2220000−2i2i2-22i−2i0000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ618-88-88000000-8-880000000000000000000000000000000000000000000000000000
χ628-88-8-400000044-400000000002i6−2i62i6−2i600000000000000000000000000000000000000
χ638-88-8-400000044-40000000000−2i62i6−2i62i600000000000000000000000000000000000000
χ648-8-888000000-88-80000000000000000000000000000000000000000000000000000
χ658-8-88-40000004-44000000000026−26−262600000000000000000000000000000000000000
χ668-8-88-40000004-440000000000−262626−2600000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.