Finite Group Databasebeta

← Group #10692639

Character table — Group #10692639

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222222344446662446666121212121212444461212121212121212124488121212122424242422444444444488
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ9111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-11-111-1-1ii−i−ii−i
χ10111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i1-1i−i11-1-1ii−i−i-11-11-1-111−i−iii−ii
χ11111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii1-11-1-1-111ii−i−i−ii
χ12111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1ii−i−i-11iiii−i−i−i−i-11−ii-1-111−i−iii-11-1111-1-1−i−iiii−i
χ13111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii1-11-111-1-1−i−iii−ii
χ14111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii1-1−ii11-1-1−i−iii-11-11-1-111ii−i−ii−i
χ15111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i1-11-1-1-111−i−iiii−i
χ16111111-1-11-1-1-1-1111-11111-1-111-1-1-1-1−i−iii-11−i−i−i−iiiii-11i−i-1-111ii−i−i-11-1111-1-1ii−i−i−ii
χ17222222222-2-2-2-22222-2-22222-2-2-2-2-2-200002-20000000000000000000022-2-20000000000
χ18222222222-2-2-2-22222-2-22222-2-2-2-2-2-200002-200000000000000000000-2-2220000000000
χ1922222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ2122222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ2222222222-12222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ23222222-2-222222222-2-2-222-2-2-2-222220000-2-2000000000000000000002-2-220000000000
χ24222222-2-222222222-2-2-222-2-2-2-222220000-2-200000000000000000000-222-20000000000
χ25222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii00000000000000
χ26222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-111112i2i−2i−2i1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i00000000000000
χ27222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i00000000000000
χ28222222-2-2-1-2-2-2-2-1-1-1-222-1-111-1-11111−2i−2i2i2i1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii00000000000000
χ292222-2-222222-2-2222-22-2-2-222-2-2-2-2222-22-2-2222-2-222-2-200000000000000000000000000
χ302222-2-222222-2-2222-22-2-2-222-2-2-2-222-22-22-22-2-222-2-22200000000000000000000000000
χ312222-2-2222-2-222222-2-22-2-2222222-2-20000-2-200000000000000000000000000002-22-200
χ322222-2-2222-2-222222-2-22-2-2222222-2-20000-2-20000000000000000000000000000-22-2200
χ332222-2-222-122-2-2-1-1-1-22-211-1-11111-1-12-22-21-1-1-111-1-1110000−i3i3−i3i3−i3i3−i3i300000000000000
χ342222-2-222-122-2-2-1-1-1-22-211-1-11111-1-12-22-21-1-1-111-1-1110000i3−i3i3−i3i3−i3i3−i300000000000000
χ352222-2-222-122-2-2-1-1-1-22-211-1-11111-1-1-22-221-111-1-111-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ362222-2-222-122-2-2-1-1-1-22-211-1-11111-1-1-22-221-111-1-111-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ372222-2-2-2-2222-2-22222-22-2-2-2-222-2-22200002-200000000000000000000000000002i−2i−2i2i00
χ382222-2-2-2-2222-2-22222-22-2-2-2-222-2-22200002-20000000000000000000000000000−2i2i2i−2i00
χ392222-2-2-2-22-2-22222222-2-2-2-2-2-2-222-2-22i−2i−2i2i222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ402222-2-2-2-22-2-22222222-2-2-2-2-2-2-222-2-2−2i2i2i−2i22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-122-2111111-1-1112i−2i−2i2i-1-1−i−iiiii−i−i0000−i3i3i3−i33−3−3300000000000000
χ422222-2-2-2-2-1-2-222-1-1-122-2111111-1-1112i−2i−2i2i-1-1−i−iiiii−i−i0000i3−i3−i3i3−333−300000000000000
χ432222-2-2-2-2-1-2-222-1-1-122-2111111-1-111−2i2i2i−2i-1-1ii−i−i−i−iii0000−i3i3i3−i3−333−300000000000000
χ442222-2-2-2-2-1-2-222-1-1-122-2111111-1-111−2i2i2i−2i-1-1ii−i−i−i−iii0000i3−i3−i3i33−3−3300000000000000
χ4544444444-2-4-4-4-4-2-2-24-4-4-2-2-2-22222220000-220000000000000000000000000000000000
χ46444444-4-4-24444-2-2-2-4-4-4-2-22222-2-2-2-20000220000000000000000000000000000000000
χ474444-4-444-2-4-444-2-2-2-4-4422-2-2-2-2-2-2220000220000000000000000000000000000000000
χ484444-4-4-4-4-244-4-4-2-2-24-442222-2-222-2-20000-220000000000000000000000000000000000
χ4944-4-44-40044i−4i4i−4i-44-40004-400004i−4i4i−4i0000000000000000000000000000000000000000
χ5044-4-44-4004−4i4i−4i4i-44-40004-40000−4i4i−4i4i0000000000000000000000000000000000000000
χ5144-4-44-400-24i−4i4i−4i2-22000-220000−2i2i−2i2i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ5244-4-44-400-24i−4i4i−4i2-22000-220000−2i2i−2i2i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ5344-4-44-400-2−4i4i−4i4i2-22000-2200002i−2i2i−2i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ5444-4-44-400-2−4i4i−4i4i2-22000-2200002i−2i2i−2i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ5544-4-4-440044i−4i−4i4i-44-4000-440000−4i4i4i−4i0000000000000000000000000000000000000000
χ5644-4-4-44004−4i4i4i−4i-44-4000-4400004i−4i−4i4i0000000000000000000000000000000000000000
χ5744-4-4-4400-24i−4i−4i4i2-220002-200002i−2i−2i2i000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000000000000000
χ5844-4-4-4400-24i−4i−4i4i2-220002-200002i−2i−2i2i000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000000000000000
χ5944-4-4-4400-2−4i4i4i−4i2-220002-20000−2i2i2i−2i000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000000000000000
χ6044-4-4-4400-2−4i4i4i−4i2-220002-20000−2i2i2i−2i000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000000000000000
χ614-4-44004-4400004-4-4000004-40000000000000000000000000000000000002i−2i2i−2i000000
χ624-4-44004-4400004-4-4000004-4000000000000000000000000000000000000−2i2i−2i2i000000
χ634-4-4400-44400004-4-400000-440000000000000000000000000000000000002i−2i−2i2i000000
χ644-4-4400-44400004-4-400000-44000000000000000000000000000000000000−2i2i2i−2i000000
χ658-88-8000080000-8-8800000000000000000000000000000000000000000000000000000
χ668-88-80000-4000044-40000000−4i34i300000000000000000000000000000000000000000000
χ678-88-80000-4000044-400000004i3−4i300000000000000000000000000000000000000000000
χ688-8-88008-8-40000-44400000-440000000000000000000000000000000000000000000000
χ698-8-8800-88-40000-444000004-40000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.