Finite Group Databasebeta

← Group #10692053

Character table — Group #10692053

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424248888242424242424242424444444888844
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
χ91111-1-111-11-1-1-111111-1-1-1111-1-11-1-1ii−i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-11-1-11ii−i−ii−ii−i1-1
χ101111-1-111-11-1-1-111111-1-1-1111-1-11-1-1ii−i−i1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1-111-1−i−iii−ii−ii-11
χ111111-1-111-11-1-1-111111-1-1-1111-1-11-1-1ii−i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-1111-1-11−i−iiii−ii−i-11
χ121111-1-111-11-1-1-111111-1-1-1111-1-11-1-1ii−i−i1-1iiii−i−i−i−i−ii-11−i−iii-1-111-111-1ii−i−i−ii−ii1-1
χ131111-1-111-11-1-1-111111-1-1-1111-1-11-1-1−i−iii1-1−i−i−i−iiiiii−i-11ii−i−i-1-1111-1-11ii−i−i−ii−ii-11
χ141111-1-111-11-1-1-111111-1-1-1111-1-11-1-1−i−iii1-1−i−i−i−iiiiii−i-11ii−i−i-1-111-111-1−i−iiii−ii−i1-1
χ151111-1-111-11-1-1-111111-1-1-1111-1-11-1-1−i−iii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-11-1-11−i−iii−ii−ii1-1
χ161111-1-111-11-1-1-111111-1-1-1111-1-11-1-1−i−iii1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1-111-1ii−i−ii−ii−i-11
χ1722222222222-2-2222-2-2-2222-2-22-222-20000-2-20000000000000000000022-2-20000000000
χ1822222222222-2-2222-2-2-2222-2-22-222-20000-2-200000000000000000000-2-2220000000000
χ192222222-2-2-2-2222222-2-222-222-22-2-222-22-2-2-222-2-222-2-200000000000000000000000000
χ202222222-2-2-2-2222222-2-222-222-22-2-22-22-22-2-2-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-200002200000000000000000000000000002i−2i−2i2i00
χ222222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000220000000000000000000000000000−2i2i2i−2i00
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ27222222-1-2-2-2-222-1-1-12-2-2-1-11-1-11-111-12-22-211-1-111-1-11100003−33−33−33−300000000000000
χ28222222-1-2-2-2-222-1-1-12-2-2-1-11-1-11-111-12-22-211-1-111-1-1110000−33−33−33−3300000000000000
χ29222222-1-2-2-2-222-1-1-12-2-2-1-11-1-11-111-1-22-221111-1-111-1-100003−33−3−33−3300000000000000
χ30222222-1-2-2-2-222-1-1-12-2-2-1-11-1-11-111-1-22-221111-1-111-1-10000−33−333−33−300000000000000
χ312222-2-222-22-222222-2-22-2-22-2-2-222-220000-22000000000000000000002-22-20000000000
χ322222-2-222-22-222222-2-22-2-22-2-2-222-220000-2200000000000000000000-22-220000000000
χ332222-2-22-22-2222222-22-2-2-2-2-2-222-22200002-2000000000000000000000000000022-2-200
χ342222-2-22-22-2222222-22-2-2-2-2-2-222-22200002-20000000000000000000000000000-2-22200
χ352222-2-22-22-22-2-22222-22-2-2-2222-2-22-22i−2i−2i2i-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-22-2-22222-22-2-2-2222-2-22-2−2i2i2i−2i-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-22-2-2-2-1-1-122-211-1-1-111-1112i2i−2i−2i-11−i−i−i−iiiii2i−2i2-2−i−iii-1-11100000000000000
χ382222-2-2-12-22-2-2-2-1-1-122-211-1-1-111-1112i2i−2i−2i-11−i−i−i−iiiii−2i2i-22ii−i−i11-1-100000000000000
χ392222-2-2-12-22-2-2-2-1-1-122-211-1-1-111-111−2i−2i2i2i-11iiii−i−i−i−i2i−2i-22−i−iii11-1-100000000000000
χ402222-2-2-12-22-2-2-2-1-1-122-211-1-1-111-111−2i−2i2i2i-11iiii−i−i−i−i−2i2i2-2ii−i−i-1-11100000000000000
χ412222-2-2-1-22-22-2-2-1-1-12-22111-1-1-111-112i−2i−2i2i1-1−i−iiiii−i−i0000−i3i3i3−i3−333−300000000000000
χ422222-2-2-1-22-22-2-2-1-1-12-22111-1-1-111-112i−2i−2i2i1-1−i−iiiii−i−i0000i3−i3−i3i33−3−3300000000000000
χ432222-2-2-1-22-22-2-2-1-1-12-22111-1-1-111-11−2i2i2i−2i1-1ii−i−i−i−iii0000−i3i3i3−i33−3−3300000000000000
χ442222-2-2-1-22-22-2-2-1-1-12-22111-1-1-111-11−2i2i2i−2i1-1ii−i−i−i−iii0000i3−i3−i3i3−333−300000000000000
χ45444444-24444-4-4-2-2-2-4-4-4-2-2-222-22-2-220000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-2-444-2-2222222220000-2-20000000000000000000000000000000000
χ474444-4-4-24-44-444-2-2-2-4-4422-2222-2-22-200002-20000000000000000000000000000000000
χ484444-4-4-2-44-4444-2-2-2-44-422222-2-22-2-20000-220000000000000000000000000000000000
χ4944-4-400400004-44-4-4000000000400-40000000000000000000000000000002-22-2000000
χ5044-4-400400004-44-4-4000000000400-4000000000000000000000000000000-22-22000000
χ5144-4-40040000-444-4-4000000000-40040000000000000000000000000000002i−2i−2i2i000000
χ5244-4-40040000-444-4-4000000000-4004000000000000000000000000000000−2i2i2i−2i000000
χ534-44-44-444-4-4400-44-40004-4400-40-4400000000000000000000000000000000000000000
χ544-44-44-44-444-400-44-40004-4-400404-400000000000000000000000000000000000000000
χ554-44-44-4-24-4-44002-22000-22-200202-200000006−66−66−66−600000000000000000000000000
χ564-44-44-4-24-4-44002-22000-22-200202-20000000−66−66−66−6600000000000000000000000000
χ574-44-44-4-2-444-4002-22000-22200-20-2200000006−6−666−6−6600000000000000000000000000
χ584-44-44-4-2-444-4002-22000-22200-20-220000000−666−6−666−600000000000000000000000000
χ594-44-4-44444-4-400-44-4000-4440040-4-400000000000000000000000000000000000000000
χ604-44-4-444-4-44400-44-4000-44-400-404400000000000000000000000000000000000000000
χ614-44-4-44-244-4-4002-220002-2-200-20220000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ624-44-4-44-244-4-4002-220002-2-200-20220000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ634-44-4-44-2-4-444002-220002-220020-2-20000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ644-44-4-44-2-4-444002-220002-220020-2-20000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6588-8-800-400008-8-444000000000-40040000000000000000000000000000000000000000
χ6688-8-800-40000-88-444000000000400-40000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-400000043−43000000000000000000000000000000000000000000000
χ698-8-8800-400000044-4000000−4343000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).