Finite Group Databasebeta

← Group #10687355

Character table — Group #10687355

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121244448888121224242424242424244444881212121224242424224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1ii−i−i1-1iiii−i−i−i−i1111i−i11-1-1ii−i−i1-1-1-11-1ii−i−ii−i
χ101111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1ii−i−i1-1iiii−i−i−i−i-1-1-1-1i−i11-1-1ii−i−i-1111-11−i−iii−ii
χ111111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1−i−iii1-1−i−i−i−iiiii1111−ii11-1-1−i−iii1-1-1-11-1−i−iii−ii
χ121111111-1-1-1-111111-1-11111-1-1-1-1-1-11-11-1−i−iii1-1−i−i−i−iiiii-1-1-1-1−ii11-1-1−i−iii-1111-11ii−i−ii−i
χ131111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11ii−i−i1-1iiii−i−i−i−i1111−ii-1-111−i−iii-11-1-1-11ii−i−i−ii
χ141111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11ii−i−i1-1iiii−i−i−i−i-1-1-1-1−ii-1-111−i−iii1-1111-1−i−iiii−i
χ151111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11−i−iii1-1−i−i−i−iiiii1111i−i-1-111ii−i−i-11-1-1-11−i−iiii−i
χ161111111-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11−i−iii1-1−i−i−i−iiiii-1-1-1-1i−i-1-111ii−i−i1-1111-1ii−i−i−ii
χ1722222222222222-2-2-2-222-2-22222-2-200000000-2-20000000022-2-20000000000002-200000000
χ1822222222222222-2-2-2-222-2-22222-2-200000000-2-200000000-2-222000000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-2-2-22200000000-220000000022-2-2000000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-2-2-22200000000-2200000000-2-2220000000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ25222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112-22-22i2i−2i−2i-11−i−i−i−iiiii00002i−2i-1-111−i−iii000000000000
χ26222222-1-2-2-2-2-1-1-122-2-2-1-1-1-11111112-22-2−2i−2i2i2i-11iiii−i−i−i−i0000−2i2i-1-111ii−i−i000000000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-22-222i2i−2i−2i-11−i−i−i−iiiii0000−2i2i11-1-1ii−i−i000000000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1111111-22-22−2i−2i2i2i-11iiii−i−i−i−i00002i−2i11-1-1−i−iii000000000000
χ292222-2-222-2-222222-22-2-2-22222-2-22200000000-2-200000000000000000000002200-2-2000000
χ302222-2-222-2-222222-22-2-2-22222-2-22200000000-2-20000000000000000000000-2-20022000000
χ312222-2-222-2-22222-22-22-2-2-2-222-2-2-2-222-2-2000022000000000000002-22-20000000000000000
χ322222-2-222-2-22222-22-22-2-2-2-222-2-2-2-2-2-22200002200000000000000-22-220000000000000000
χ332222-2-22-222-22222-2-22-2-222-2-222-2-200000000-2200000000000000000000002-200-22000000
χ342222-2-22-222-22222-2-22-2-222-2-222-2-200000000-220000000000000000000000-22002-2000000
χ352222-2-22-222-2222-222-2-2-2-2-2-2-222222-2-2200002-2000000000000002-2-220000000000000000
χ362222-2-22-222-2222-222-2-2-2-2-2-2-22222-222-200002-200000000000000-222-20000000000000000
χ372222-2-2-12-2-22-1-1-1-22-221111-1-1111122-2-20000-1-133−3−333−3−3000000-11-113−33−3000000000000
χ382222-2-2-12-2-22-1-1-1-22-221111-1-1111122-2-20000-1-1−3−333−3−333000000-11-11−33−33000000000000
χ392222-2-2-12-2-22-1-1-1-22-221111-1-11111-2-2220000-1-133−3−333−3−30000001-11-1−33−33000000000000
χ402222-2-2-12-2-22-1-1-1-22-221111-1-11111-2-2220000-1-1−3−333−3−3330000001-11-13−33−3000000000000
χ412222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-12-2-220000-11−i3−i3i3i3i3i3−i3−i3000000-111-1−i3i3i3−i3000000000000
χ422222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-12-2-220000-11i3i3−i3−i3−i3−i3i3i3000000-111-1i3−i3−i3i3000000000000
χ432222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-1-222-20000-11−i3−i3i3i3i3i3−i3−i30000001-1-11i3−i3−i3i3000000000000
χ442222-2-2-1-222-2-1-1-1-222-2111111-1-1-1-1-222-20000-11i3i3−i3−i3−i3−i3i3i30000001-1-11−i3i3i3−i3000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-4-444-2-2222222-2-2000000002-20000000000000000000000000000000000
χ474444-4-4-24-4-44-2-2-24-44-422-2-2-2-222-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-444-4-2-2-24-4-4422-2-222-2-222000000002-20000000000000000000000000000000000
χ4944-4-4004400-4-44-4000000004-4000000002-22-2002-22-22-22-200000000000000000000000000
χ5044-4-4004400-4-44-4000000004-400000000-22-2200-22-22-22-2200000000000000000000000000
χ5144-4-4004-4004-44-400000000-44000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4004-4004-44-400000000-4400000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-400-2400-42-2200000023−23-220023−2300002-22-200−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000000000
χ5444-4-400-2400-42-2200000023−23-220023−230000-22-22001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000000000
χ5544-4-400-2400-42-22000000−2323-2200−232300002-22-200−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000000000
χ5644-4-400-2400-42-22000000−2323-2200−23230000-22-22001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000000000
χ5744-4-400-2-40042-2200000023−232-200−232300002i−2i−2i2i00ζ4+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
χ5844-4-400-2-40042-2200000023−232-200−23230000−2i2i2i−2i00−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
χ5944-4-400-2-40042-22000000−23232-20023−2300002i−2i−2i2i00−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
χ6044-4-400-2-40042-22000000−23232-20023−230000−2i2i2i−2i00ζ4−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
χ614-44-400404i−4i0-4-4400000000004i−4i00000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ624-44-400404i−4i0-4-4400000000004i−4i0000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ634-44-40040−4i4i0-4-440000000000−4i4i0000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ644-44-40040−4i4i0-4-440000000000−4i4i00000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ654-4-444-4400004-4-400004-400000000000000000000000000004i−4i0000000000000000000000
χ664-4-444-4400004-4-400004-40000000000000000000000000000−4i4i0000000000000000000000
χ674-4-44-44400004-4-40000-44000000000000000000000000004i−4i000000000000000000000000
χ684-4-44-44400004-4-40000-4400000000000000000000000000−4i4i000000000000000000000000
χ698-88-800-408i−8i044-40000000000−4i4i0000000000000000000000000000000000000000000000
χ708-88-800-40−8i8i044-400000000004i−4i0000000000000000000000000000000000000000000000
χ718-8-888-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ728-8-88-88-40000-44400004-40000000000000000000000000000000000000000000000000000

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