Finite Group Databasebeta

← Group #10767975

Character table — Group #10767975

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222234444666444466121212121212121244444444121212121212121212122222881212121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-111-1-1-111111-1-1-1-111-1-11-111-1-111-1-1111-11-11-1-1-11-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-111-1-1-111111-1-1-1-1-1-1111-111-1-111-1-1-1-1-11-11-1111-11
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-1-1-111-11-1-1-1-1111111-1-1-1111-1-1-1-111-1-11-11-11-111-11
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-1111-11-1-1-111-11-1-1-1-11111-1-111-1111-1-1-1-11111-11-11-11-1-11-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1111-1-1-111111-1-1-1-111-1-1-11-1-111-1-11111-111-1-11-1-1-11
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1111-1-1-111111-1-1-1-1-1-111-11-1-111-1-111-1-11-1-111-1111-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-11-1-111-11-1-1-1-1111111-1-11-1-1-11111-1-1-1-1-111-1-11111-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-11-1-111-11-1-1-1-11111-1-1111-1-1-11111-1-1111-1-111-1-1-1-11
χ1722222222222222-2-2-2-222-2-22222-2-200000000-2-20000000022-2-200000000000000-22000000
χ1822222222222222-2-2-2-222-2-22222-2-200000000-2-200000000-2-222000000000000002-2000000
χ192222222-2-2-2-222222-2-22222-2-2-2-2-2-2000000002-200000000222200000000000000-2-2000000
χ202222222-2-2-2-222222-2-22222-2-2-2-2-2-2000000002-200000000-2-2-2-20000000000000022000000
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
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-222-2-21-1-1-1-1-1111100002-2-1-111-1-111000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-12-22-2-2-2221-11111-1-1-1-10000-22-1-11111-1-1000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-2222-2-21-1-1-1-1-111110000-2211-1-111-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-22-22-2-2221-11111-1-1-1-100002-211-1-1-1-111000000000000
χ292222-2-2222-2-22222-22-2-2-22222-2-22200000000-2-20000000000000000000000002200-2-20000
χ302222-2-2222-2-22222-22-2-2-22222-2-22200000000-2-2000000000000000000000000-2-200220000
χ312222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-222-2-2000022000000000000002-22-20000000000000000
χ322222-2-2222-2-2222-22-22-2-2-2-222-2-2-2-2-2-22200002200000000000000-22-220000000000000000
χ332222-2-22-2-2222222-2-22-2-222-2-222-2-22-2-220000-22000000000000002-2-220000000000000000
χ342222-2-22-2-2222222-2-22-2-222-2-222-2-2-222-20000-2200000000000000-222-20000000000000000
χ352222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-20000000000000000000000002-200-220000
χ362222-2-22-2-222222-222-2-2-2-2-2-2-22222000000002-2000000000000000000000000-22002-20000
χ372222-2-2-122-2-2-1-1-1-22-221111-1-1111122-2-20000-1-133−3−333−3−3000000-11-113−33−3000000000000
χ382222-2-2-122-2-2-1-1-1-22-221111-1-1111122-2-20000-1-1−3−333−3−333000000-11-11−33−33000000000000
χ392222-2-2-122-2-2-1-1-1-22-221111-1-11111-2-2220000-1-133−3−333−3−30000001-11-1−33−33000000000000
χ402222-2-2-122-2-2-1-1-1-22-221111-1-11111-2-2220000-1-1−3−333−3−3330000001-11-13−33−3000000000000
χ412222-2-2-1-2-222-1-1-12-2-2211-1-111-1-1112-2-2200001-133−3−3−3−333000000-111-13−3−33000000000000
χ422222-2-2-1-2-222-1-1-12-2-2211-1-111-1-1112-2-2200001-1−3−33333−3−3000000-111-1−333−3000000000000
χ432222-2-2-1-2-222-1-1-12-2-2211-1-111-1-111-222-200001-133−3−3−3−3330000001-1-11−333−3000000000000
χ442222-2-2-1-2-222-1-1-12-2-2211-1-111-1-111-222-200001-1−3−33333−3−30000001-1-113−3−33000000000000
χ45444444-24444-2-2-2-4-4-4-4-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-244-4-4-2-2-2-222222200000000-220000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-24-44-422-2-2-2-222-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-2-444-4222222-2-2-2-200000000-220000000000000000000000000000000000
χ4944-4-44-4400004-4-400004-4000000000000000000000000004-4000000000000000000000000
χ5044-4-44-4400004-4-400004-400000000000000000000000000-44000000000000000000000000
χ5144-4-4-44400004-4-40000-4400000000000000000000000000004-40000000000000000000000
χ5244-4-4-44400004-4-40000-440000000000000000000000000000-440000000000000000000000
χ534-44-4004004i−4i-44-400000000004i−4i00000000000000000000000000000000002-20000002i−2i00
χ544-44-4004004i−4i-44-400000000004i−4i0000000000000000000000000000000000-22000000−2i2i00
χ554-44-400400−4i4i-44-40000000000−4i4i00000000000000000000000000000000002-2000000−2i2i00
χ564-44-400400−4i4i-44-40000000000−4i4i0000000000000000000000000000000000-220000002i−2i00
χ574-4-440044-400-4-44000000004-4000000002-22-2002-22-22-22-200000000000000000000000000
χ584-4-440044-400-4-44000000004-400000000-22-2200-22-22-22-2200000000000000000000000000
χ594-4-44004-4400-4-4400000000-44000000002-2-22002-22-2-22-2200000000000000000000000000
χ604-4-44004-4400-4-4400000000-4400000000-222-200-22-222-22-200000000000000000000000000
χ614-4-4400-24-40022-200000023−23-220023−2300002-22-200−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000000000
χ624-4-4400-24-40022-200000023−23-220023−230000-22-22001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000000000
χ634-4-4400-24-40022-2000000−2323-2200−232300002-22-200−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000000000
χ644-4-4400-24-40022-2000000−2323-2200−23230000-22-22001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000000000
χ654-4-4400-2-440022-200000023−232-200−232300002-2-2200−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000000000
χ664-4-4400-2-440022-200000023−232-200−23230000-222-2001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000000000
χ674-4-4400-2-440022-2000000−23232-20023−2300002-2-2200−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000000000
χ684-4-4400-2-440022-2000000−23232-20023−230000-222-2001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000000000
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i4-440000000000−4i4i0000000000000000000000000000000000000000000000
χ728-88-800-400−8i8i4-4400000000004i−4i0000000000000000000000000000000000000000000000

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