Finite Group Databasebeta

← Group #10712000

Character table — Group #10712000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444444444448888888888888888888888121212121212121216161616161616162424242448484848
order124423461212222444444466612121224668888121212121212242424242424242488888888446121212121288884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111-1-1-1-1111111-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111
χ81111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11111-1-1
χ911-1-111-11-1-1-1111-1-111-1-11-1-111-11-111ii−i−i-1-111-1-1iiii−i−i−i−iii−i−iii−i−ii−i1-1ii−i−ii−ii−i1-11-1
χ1011-1-111-11-1-1-1111-1-111-1-11-1-111-11-111ii−i−i-1-111-1-1iiii−i−i−i−i−i−iii−i−iiii−i1-1ii−i−i−ii−ii-11-11
χ1111-1-111-11-1-1-1111-1-111-1-11-1-111-11-111−i−iii-1-111-1-1−i−i−i−iiiiiii−i−iii−i−i−ii1-1−i−iiii−ii−i-11-11
χ1211-1-111-11-1-1-1111-1-111-1-11-1-111-11-111−i−iii-1-111-1-1−i−i−i−iiiii−i−iii−i−iii−ii1-1−i−iii−ii−ii1-11-1
χ1311-1-111-11-1-1-1111-1-1-1-1111-1-111-1-1111ii−i−i-1-1-1-111iiii−i−i−i−iii−i−i−i−iii−ii-11−i−iiii−i−ii1-1-11
χ1411-1-111-11-1-1-1111-1-1-1-1111-1-111-1-1111ii−i−i-1-1-1-111iiii−i−i−i−i−i−iiiii−i−i−ii-11−i−iii−iii−i-111-1
χ1511-1-111-11-1-1-1111-1-1-1-1111-1-111-1-1111−i−iii-1-1-1-111−i−i−i−iiiiiii−i−i−i−iiii−i-11ii−i−ii−i−ii-111-1
χ1611-1-111-11-1-1-1111-1-1-1-1111-1-111-1-1111−i−iii-1-1-1-111−i−i−i−iiiii−i−iiiii−i−ii−i-11ii−i−i−iii−i1-1-11
χ1722222222222-2-22-2-22222222222-2-2-2-20000-2-22222000000000000000000-2-2000000000000
χ1822222222222-2-22-2-2-2-2-2-222222222-2-20000-2-2-2-2-2-200000000000000000022000000000000
χ192222222222-22-2-22-200002-2-2-2-22002-200002-2000000000000000022220000000000-2-20000
χ202222222222-22-2-22-200002-2-2-2-22002-200002-20000000000000000-2-2-2-20000000000220000
χ212222222222-2-22-2-2200002-2-2-2-2200-220000-220000000000002222000000000000-2-2000000
χ222222222222-2-22-2-2200002-2-2-2-2200-220000-22000000000000-2-2-2-200000000000022000000
χ2322222-12-1-1-12222222222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-100000000
χ2422222-12-1-1-12222222222-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-2-1-1111100000000
χ2522222-12-1-1-1222222-2-2-2-2-1-1-1-1-1-1-2-2-1-12222-1-11111-1-1-1-1-1-1-1-100000000-2-211111100000000
χ2622222-12-1-1-1222222-2-2-2-2-1-1-1-1-1-1-2-2-1-1-2-2-2-2-1-1111111111111000000002211-1-1-1-100000000
χ2722222-12-1-1-12-2-22-2-22222-1-1-1-1-1-1-2-211000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000011−i3i3−i3i300000000
χ2822222-12-1-1-12-2-22-2-22222-1-1-1-1-1-1-2-211000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000011i3−i3i3−i300000000
χ2922222-12-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-122110000111111−i3−i3i3i3−i3−i3i3i30000000000-1-1i3−i3i3−i300000000
χ3022222-12-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-122110000111111i3i3−i3−i3i3i3−i3−i30000000000-1-1−i3i3−i3i300000000
χ3122-2-222-22-2-222-2-2-220000222-2-2-2002-20000-2200000000000000002i2i−2i−2i0000000000−2i2i0000
χ3222-2-222-22-2-222-2-2-220000222-2-2-2002-20000-220000000000000000−2i−2i2i2i00000000002i−2i0000
χ3322-2-222-22-2-22-22-22-20000222-2-2-200-2200002-20000000000002i2i−2i−2i000000000000−2i2i000000
χ3422-2-222-22-2-22-22-22-20000222-2-2-200-2200002-2000000000000−2i−2i2i2i0000000000002i−2i000000
χ3522-2-222-22-2-2-2-2-222222-2-22-2-222-2-22-2-200002222-2-2000000000000000000-22000000000000
χ3622-2-222-22-2-2-2-2-2222-2-2222-2-222-22-2-2-2000022-2-2220000000000000000002-2000000000000
χ3722-2-22-1-2-111-2222-2-222-2-2-111-1-112-2-1-12i2i−2i−2i11-1-111−i−i−i−iiiii000000002i−2i-11−i−iii00000000
χ3822-2-22-1-2-111-2222-2-222-2-2-111-1-112-2-1-1−2i−2i2i2i11-1-111iiii−i−i−i−i00000000−2i2i-11ii−i−i00000000
χ3922-2-22-1-2-111-2222-2-2-2-222-111-1-11-22-1-12i2i−2i−2i1111-1-1−i−i−i−iiiii00000000−2i2i1-1ii−i−i00000000
χ4022-2-22-1-2-111-2222-2-2-2-222-111-1-11-22-1-1−2i−2i2i2i1111-1-1iiii−i−i−i−i000000002i−2i1-1−i−iii00000000
χ4122-2-22-1-2-111-2-2-222222-2-2-111-1-11-22110000-1-1-1-11133−3−3−3−33300000000001-13−3−3300000000
χ4222-2-22-1-2-111-2-2-222222-2-2-111-1-11-22110000-1-1-1-111−3−33333−3−300000000001-1−333−300000000
χ4322-2-22-1-2-111-2-2-2222-2-222-111-1-112-2110000-1-111-1-133−3−3−3−3330000000000-11−333−300000000
χ4422-2-22-1-2-111-2-2-2222-2-222-111-1-112-2110000-1-111-1-1−3−33333−3−30000000000-113−3−3300000000
χ4544444-24-2-2-2-44-4-44-40000-22222-200-220000-22000000000000000000000000000000000000
χ4644444-24-2-2-2-4-44-4-440000-22222-2002-200002-2000000000000000000000000000000000000
χ474444-44-44440000000000-40000-400002-22-20000002-22-22-22-2000000000000000000000000
χ484444-44-44440000000000-40000-40000-22-22000000-22-22-22-22000000000000000000000000
χ494444-4-2-4-2-2-200000000002−2i32i3−2i32i3200002-22-2000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000
χ504444-4-2-4-2-2-200000000002−2i32i3−2i32i320000-22-220000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000
χ514444-4-2-4-2-2-2000000000022i3−2i32i3−2i3200002-22-2000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000
χ524444-4-2-4-2-2-2000000000022i3−2i32i3−2i320000-22-220000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000
χ5344-4-44-2-4-22244-4-4-440000-2-2-222200-2200002-2000000000000000000000000000000000000
χ5444-4-44-2-4-2224-44-44-40000-2-2-2222002-20000-22000000000000000000000000000000000000
χ5544-4-4-4444-4-40000000000-40000400002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5644-4-4-4444-4-40000000000-4000040000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5744-4-4-4-24-22200000000002−2i32i32i3−2i3-200002i−2i−2i2i0000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ22000000000000000000000000
χ5844-4-4-4-24-22200000000002−2i32i32i3−2i3-20000−2i2i2i−2i000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ22000000000000000000000000
χ5944-4-4-4-24-222000000000022i3−2i3−2i32i3-200002i−2i−2i2i0000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ14000000000000000000000000
χ6044-4-4-4-24-222000000000022i3−2i3−2i32i3-20000−2i2i2i−2i000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ14000000000000000000000000
χ614-44i−4i040-44i−4i0000002-22i−2i00000000000000002-22i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ624-44i−4i040-44i−4i0000002-22i−2i00000000000000002-22i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ634-44i−4i040-44i−4i000000-22−2i2i0000000000000000-22−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ644-44i−4i040-44i−4i000000-22−2i2i0000000000000000-22−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ654-4−4i4i040-4−4i4i0000002-2−2i2i00000000000000002-2−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ664-4−4i4i040-4−4i4i0000002-2−2i2i00000000000000002-2−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ674-4−4i4i040-4−4i4i000000-222i−2i0000000000000000-222i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ684-4−4i4i040-4−4i4i000000-222i−2i0000000000000000-222i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ698-88i−8i0-404−4i4i0000004-44i−4i0000000000000000-22−2i2i00000000000000000000000000000000
χ708-88i−8i0-404−4i4i000000-44−4i4i00000000000000002-22i−2i00000000000000000000000000000000
χ718-8−8i8i0-4044i−4i0000004-4−4i4i0000000000000000-222i−2i00000000000000000000000000000000
χ728-8−8i8i0-4044i−4i000000-444i−4i00000000000000002-2−2i2i00000000000000000000000000000000

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