Finite Group Databasebeta

← Group #10692018

Character table — Group #10692018

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122234444444466624412121212121212121212688881224242424242424248888242424242424242424448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−ii−i1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1
χ101111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-1-111−i−iii−i−iii-11
χ111111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i−ii-11−i−iii-1-11111-1-1−i−iiiii−i−i-11
χ121111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1ii−i−i1iiii−i−i−i−i−ii-11−i−iii-1-111-1-111ii−i−i−i−iii1-1
χ131111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiiii−i-11ii−i−i-1-11111-1-1ii−i−i−i−iii-11
χ141111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiiii−i-11ii−i−i-1-111-1-111−i−iiiii−i−i1-1
χ151111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii−ii1-1−i−iii11-1-111-1-1−i−iii−i−iii1-1
χ161111111-1-1-1-1-1-1111-11111-1-111-1-1-1-1-1−i−iii1−i−i−i−iiiii−ii1-1−i−iii11-1-1-1-111ii−i−iii−i−i-11
χ1722222222222-2-2222-2-2-2-2-2222222-2-2-20000-2000000000000000000002-22-20000000000
χ1822222222222-2-2222-2-2-2-2-2222222-2-2-20000-200000000000000000000-22-220000000000
χ192222222-2-2-2-2222222-2-2-2-2-2-222-2-22220000-2000000000000000000002-2-220000000000
χ202222222-2-2-2-2222222-2-2-2-2-2-222-2-22220000-200000000000000000000-222-20000000000
χ2122222-2-222-2-222222-22-2-2-2-2-2-2-22222-20000200000000000000000000000000002-22-200
χ2222222-2-222-2-222222-22-2-2-2-2-2-2-22222-2000020000000000000000000000000000-22-2200
χ2322222-2-222-2-2-2-22222-2222-2-2-2-222-2-222i−2i2i−2i-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ2422222-2-222-2-2-2-22222-2222-2-2-2-222-2-22−2i2i−2i2i-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ2522222-2-2-2-22222222-2-222222-2-2-2-222-22-2-22-222-2-2-2-22200000000000000000000000000
χ2622222-2-2-2-22222222-2-222222-2-2-2-222-2-222-2-2-2-22222-2-200000000000000000000000000
χ2722222-2-2-2-222-2-222222-2-2-222-2-2-2-2-2-220000200000000000000000000000000002i−2i−2i2i00
χ2822222-2-2-2-222-2-222222-2-2-222-2-2-2-2-2-22000020000000000000000000000000000−2i2i2i−2i00
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111111122-2-2-1-1-1-1111100000000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-111111111-2-2221111-1-1-1-100000000000000
χ332222-122-2-2-2-2-2-2-1-1-1-222-1-111-1-1111112i2i−2i−2i-1−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ342222-122-2-2-2-2-2-2-1-1-1-222-1-111-1-1111112i2i−2i−2i-1−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ352222-122-2-2-2-2-2-2-1-1-1-222-1-111-1-111111−2i−2i2i2i-1iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ362222-122-2-2-2-2-2-2-1-1-1-222-1-111-1-111111−2i−2i2i2i-1iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ372222-1-2-222-2-2-2-2-1-1-12-22-1-11111-1-111-12i−2i2i−2i1−i−iii−i−iii0000−i3i3−i3i33−33−300000000000000
χ382222-1-2-222-2-2-2-2-1-1-12-22-1-11111-1-111-12i−2i2i−2i1−i−iii−i−iii0000i3−i3i3−i3−33−3300000000000000
χ392222-1-2-222-2-2-2-2-1-1-12-22-1-11111-1-111-1−2i2i−2i2i1ii−i−iii−i−i0000−i3i3−i3i3−33−3300000000000000
χ402222-1-2-222-2-2-2-2-1-1-12-22-1-11111-1-111-1−2i2i−2i2i1ii−i−iii−i−i0000i3−i3i3−i33−33−300000000000000
χ412222-1-2-2-2-22222-1-1-1-2-22-1-1-1-11111-1-112-2-221-1-11111-1-100003−3−33−333−300000000000000
χ422222-1-2-2-2-22222-1-1-1-2-22-1-1-1-11111-1-112-2-221-1-11111-1-10000−333−33−3−3300000000000000
χ432222-1-2-2-2-22222-1-1-1-2-22-1-1-1-11111-1-11-222-2111-1-1-1-11100003−3−333−3−3300000000000000
χ442222-1-2-2-2-22222-1-1-1-2-22-1-1-1-11111-1-11-222-2111-1-1-1-1110000−333−3−333−300000000000000
χ454444-2444444-4-4-2-2-2-4-4-422-2-2-2-2-2-2222000020000000000000000000000000000000000
χ464444-244-4-4-4-444-2-2-24-4-42222-2-222-2-2-2000020000000000000000000000000000000000
χ474444-2-4-444-4-444-2-2-2-44-4222222-2-2-2-220000-20000000000000000000000000000000000
χ484444-2-4-4-4-444-4-4-2-2-244-422-2-2222222-20000-20000000000000000000000000000000000
χ494-44-440000004i−4i4-4-4000000000004i−4i0000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ504-44-440000004i−4i4-4-4000000000004i−4i000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ514-44-44000000−4i4i4-4-400000000000−4i4i000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ524-44-44000000−4i4i4-4-400000000000−4i4i0000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ534-4-4444-44i−4i4i−4i00-44-4000004i−4i4-44i−4i000000000000000000000000000000000000000000
χ544-4-4444-4−4i4i−4i4i00-44-400000−4i4i4-4−4i4i000000000000000000000000000000000000000000
χ554-4-444-444i−4i−4i4i00-44-400000−4i4i-444i−4i000000000000000000000000000000000000000000
χ564-4-444-44−4i4i4i−4i00-44-4000004i−4i-44−4i4i000000000000000000000000000000000000000000
χ574-4-44-24-44i−4i4i−4i002-2200000−2i2i-22−2i2i00000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000
χ584-4-44-24-44i−4i4i−4i002-2200000−2i2i-22−2i2i00000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000
χ594-4-44-24-4−4i4i−4i4i002-22000002i−2i-222i−2i00000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000
χ604-4-44-24-4−4i4i−4i4i002-22000002i−2i-222i−2i00000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000
χ614-4-44-2-444i−4i−4i4i002-22000002i−2i2-2−2i2i00000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000
χ624-4-44-2-444i−4i−4i4i002-22000002i−2i2-2−2i2i00000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000
χ634-4-44-2-44−4i4i4i−4i002-2200000−2i2i2-22i−2i00000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000
χ644-4-44-2-44−4i4i4i−4i002-2200000−2i2i2-22i−2i00000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000
χ6588-8-8800000000-8-8800000000000000000000000000000000000000000000000000000
χ6688-8-8-40000000044-400043−43000000000000000000000000000000000000000000000000
χ6788-8-8-40000000044-4000−4343000000000000000000000000000000000000000000000000
χ688-88-8-40000008i−8i-44400000000000−4i4i0000000000000000000000000000000000000000
χ698-88-8-4000000−8i8i-444000000000004i−4i0000000000000000000000000000000000000000

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