Finite Group Databasebeta

← Group #10694902

Character table — Group #10694902

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222222344444466624666612121212121244446121212121212121212888888884488121212122424242488882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ9111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−i1-1i−i
χ10111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iiiii−i−i-11−ii
χ11111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-1-1-1-111111-1i−i11-1-1ii−i−i−i−iii-11−ii
χ12111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-1-1-1-11111-11−ii-1-111−i−iii−i−iii1-1i−i
χ13111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii1-1−ii
χ14111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i−i−iii-11i−i
χ15111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-1-1-1-111111-1−ii11-1-1−i−iiiii−i−i-11i−i
χ16111111-1-111-1-1-1-11111-1111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-1-1-1-11111-11i−i-1-111ii−i−iii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-200002-200000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-200002-20000000000000000000000000000−2i2i−2i2i0000
χ1922222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ2022222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ2122222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ2222222222-1222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ23222222-2-22-22222-2222-2-222-2-2-2-222220000-2-200000000000000000000000000002-2-220000
χ24222222-2-22-22222-2222-2-222-2-2-2-222220000-2-20000000000000000000000000000-222-20000
χ25222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii000000002-22i−2i-1-111−i−iii00000000
χ26222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii00000000-22−2i2i11-1-1ii−i−i00000000
χ27222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i000000002-2−2i2i-1-111ii−i−i00000000
χ28222222-2-2-12-2-2-2-22-1-1-1-22-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i00000000-222i−2i11-1-1−i−iii00000000
χ292222-2-2222222-2-22222-2-2-2-2222222-2-20000-2-20000000022-2-222-2-200000000000000000000
χ302222-2-2222222-2-22222-2-2-2-2222222-2-20000-2-200000000-2-222-2-22200000000000000000000
χ312222-2-2222-2-2-222-2222-22-2-222-2-2-2-2222-22-2-2222-2-222-2-20000000000000000000000000000
χ322222-2-2222-2-2-222-2222-22-2-222-2-2-2-222-22-22-22-2-222-2-2220000000000000000000000000000
χ332222-2-222-1-2-2-222-2-1-1-1-2211-1-11111-1-12-22-21-1-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i300000000
χ342222-2-222-1-2-2-222-2-1-1-1-2211-1-11111-1-12-22-21-1-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i300000000
χ352222-2-222-1-2-2-222-2-1-1-1-2211-1-11111-1-1-22-221-111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ362222-2-222-1-2-2-222-2-1-1-1-2211-1-11111-1-1-22-221-111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ372222-2-2-2-222-2-22222222-2-2-2-2-222-2-22200002-20000000022-2-2-2-22200000000000000000000
χ382222-2-2-2-222-2-22222222-2-2-2-2-222-2-22200002-200000000-2-22222-2-200000000000000000000
χ392222-2-2-2-22-222-2-2-222222-2-2-2-2-2-222-2-22i−2i−2i2i222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-2-22-222-2-2-222222-2-2-2-2-2-222-2-2−2i2i2i−2i22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-2-2-1-222-2-2-2-1-1-122111111-1-1112i−2i−2i2i-1-1−i−iiiii−i−i000000000000−i3i3i3−i33−3−3300000000
χ422222-2-2-2-2-1-222-2-2-2-1-1-122111111-1-1112i−2i−2i2i-1-1−i−iiiii−i−i000000000000i3−i3−i3i3−333−300000000
χ432222-2-2-2-2-1-222-2-2-2-1-1-122111111-1-111−2i2i2i−2i-1-1ii−i−i−i−iii000000000000−i3i3i3−i3−333−300000000
χ442222-2-2-2-2-1-222-2-2-2-1-1-122111111-1-111−2i2i2i−2i-1-1ii−i−i−i−iii000000000000i3−i3−i3i33−3−3300000000
χ4544444444-2-4-4-4-4-4-4-2-2-24-4-2-2-2-22222220000-22000000000000000000000000000000000000
χ46444444-4-4-2-44444-4-2-2-2-4-4-2-22222-2-2-2-2000022000000000000000000000000000000000000
χ474444-4-444-2444-4-44-2-2-2-4-422-2-2-2-2-2-222000022000000000000000000000000000000000000
χ484444-4-4-4-4-24-4-4444-2-2-24-42222-2-222-2-20000-22000000000000000000000000000000000000
χ4944-4-44-400404i−4i4i−4i0-44-4004-400004i−4i4i−4i000000000000000000000000000000000000000000
χ5044-4-44-40040−4i4i−4i4i0-44-4004-40000−4i4i−4i4i000000000000000000000000000000000000000000
χ5144-4-44-400-204i−4i4i−4i02-2200-220000−2i2i−2i2i000000−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+ζ220000000000000000000000000000
χ5244-4-44-400-204i−4i4i−4i02-2200-220000−2i2i−2i2i000000ζ4+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−ζ220000000000000000000000000000
χ5344-4-44-400-20−4i4i−4i4i02-2200-2200002i−2i2i−2i000000−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−ζ220000000000000000000000000000
χ5444-4-44-400-20−4i4i−4i4i02-2200-2200002i−2i2i−2i000000ζ4−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+ζ220000000000000000000000000000
χ5544-4-4-4400404i−4i−4i4i0-44-400-4400004i−4i−4i4i000000000000000000000000000000000000000000
χ5644-4-4-440040−4i4i4i−4i0-44-400-440000−4i4i4i−4i000000000000000000000000000000000000000000
χ5744-4-4-4400-204i−4i−4i4i02-22002-20000−2i2i2i−2i000000−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+ζ220000000000000000000000000000
χ5844-4-4-4400-204i−4i−4i4i02-22002-20000−2i2i2i−2i000000ζ4−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−ζ220000000000000000000000000000
χ5944-4-4-4400-20−4i4i4i−4i02-22002-200002i−2i−2i2i000000−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−ζ220000000000000000000000000000
χ6044-4-4-4400-20−4i4i4i−4i02-22002-200002i−2i−2i2i000000ζ4+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+ζ220000000000000000000000000000
χ614-44-40000440000-4-4-440000004-4000000000000000000004i−4i000000000000000000000000
χ624-44-40000440000-4-4-440000004-400000000000000000000−4i4i000000000000000000000000
χ634-44-400004-400004-4-44000000-440000000000000000000000004-400000000000000000000
χ644-44-400004-400004-4-44000000-44000000000000000000000000-4400000000000000000000
χ654-4-44004-440000004-4-400004-400000000000000000000−2i22i200−2i22i20000000000000000000000
χ664-4-44004-440000004-4-400004-4000000000000000000002i2−2i2002i2−2i20000000000000000000000
χ674-4-4400-4440000004-4-40000-4400000000000000000000−2i22i2002i2−2i20000000000000000000000
χ684-4-4400-4440000004-4-40000-44000000000000000000002i2−2i200−2i22i20000000000000000000000
χ698-88-80000-480000-844-4000000-440000000000000000000000000000000000000000000000
χ708-88-80000-4-80000844-40000004-40000000000000000000000000000000000000000000000
χ718-8-88008-8-4000000-4440000-44000000000000000000000000000000000000000000000000
χ728-8-8800-88-4000000-44400004-4000000000000000000000000000000000000000000000000

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