Finite Group Databasebeta

← Group #10769016

Character table — Group #10769016

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order12222234444666444466121212121212121244444444121212121212121212128812121212242424242244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-11-11-1-1111111-1-1-1-1
χ91111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-1-111111-1-1-1-11-111-1-111-1-111-111-1-1-111-1-111-1-1
χ101111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-1-111111-1-1-1-11-111-1-111-1-1-1-11-1-1111-1-111-1-111
χ111111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111-11-1-1-1-11111-1111-1-1-1-11111-111-1-1-1-1-111-1-111
χ121111111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-111-11-1-1-1-11111-1111-1-1-1-111-1-11-1-111111-1-111-1-1
χ131111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-1-111111-1-1-1-1-11-1-111-1-1111-1-1-11-11111-1-1-1-111
χ141111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-1-111111-1-1-1-1-11-1-111-1-111-1111-11-1-1-1-11111-1-1
χ151111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-111-11-1-1-1-111111-1-1-11111-1-11-1-1-11-111-1-11111-1-1
χ161111111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-111-1-111-11-1-1-1-111111-1-1-11111-1-1-1111-11-1-111-1-1-1-111
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-2000000002-200000000000000000020-20-220000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2000000002-2000000000000000000-20202-20000000000
χ192222222-2-222222-22-2-222-2-22222-2-200000000-2-20000000000000000002020-2-20000000000
χ202222222-2-222222-22-2-222-2-22222-2-200000000-2-2000000000000000000-20-20220000000000
χ21222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-2-1-1-1-111110000000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111221111-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-222-2-21-1-1-1-1-111112-2-1-111-1-1110000000000000000
χ26222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-122-2-2-2-2221-11111-1-1-1-1-22-1-11111-1-10000000000000000
χ27222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-22222-2-21-1-1-1-1-11111-2211-1-111-1-10000000000000000
χ28222222-1-2-2-2-2-1-1-1-2-222-1-1111111-1-1-2-222-2-2221-11111-1-1-1-12-211-1-1-1-1110000000000000000
χ292222-2-222222222-2-2-22-2-22222-2-2-2-22-22-20000-2200000000002-22-200000000000000000000
χ302222-2-222222222-2-2-22-2-22222-2-2-2-2-22-220000-220000000000-22-2200000000000000000000
χ312222-2-2222-2-2222-222-2-2-222-2-2222200000000-2-2000000000000000000020-2002-200000000
χ322222-2-2222-2-2222-222-2-2-222-2-2222200000000-2-20000000000000000000-20200-2200000000
χ332222-2-22-2-2222222-22-2-2-2-2-222-2-222000000002-2000000000000000000020-200-2200000000
χ342222-2-22-2-2222222-22-2-2-2-2-222-2-222000000002-20000000000000000000-202002-200000000
χ352222-2-22-2-2-2-222222-22-2-2-2-2-2-222-2-22-2-2200002200000000002-2-2200000000000000000000
χ362222-2-22-2-2-2-222222-22-2-2-2-2-2-222-2-2-222-20000220000000000-222-200000000000000000000
χ372222-2-2-12222-1-1-1-2-2-2211-1-1-1-111112-22-200001-133−3−333−3−300-11-113−33−30000000000000000
χ382222-2-2-12222-1-1-1-2-2-2211-1-1-1-111112-22-200001-1−3−333−3−33300-11-11−33−330000000000000000
χ392222-2-2-12222-1-1-1-2-2-2211-1-1-1-11111-22-2200001-133−3−333−3−3001-11-1−33−330000000000000000
χ402222-2-2-12222-1-1-1-2-2-2211-1-1-1-11111-22-2200001-1−3−333−3−333001-11-13−33−30000000000000000
χ412222-2-2-1-2-2-2-2-1-1-122-22111111-1-1112-2-220000-1-133−3−3−3−33300-111-13−3−330000000000000000
χ422222-2-2-1-2-2-2-2-1-1-122-22111111-1-1112-2-220000-1-1−3−33333−3−300-111-1−333−30000000000000000
χ432222-2-2-1-2-2-2-2-1-1-122-22111111-1-111-222-20000-1-133−3−3−3−333001-1-11−333−30000000000000000
χ442222-2-2-1-2-2-2-2-1-1-122-22111111-1-111-222-20000-1-1−3−33333−3−3001-1-113−3−330000000000000000
χ45444444-244-4-4-2-2-24-4-4-4-2-2-2-222222200000000-220000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-44-4-4-2-222-2-2-2-22200000000220000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-444-422-2-222-2-2-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-24-44-42222-2-222-2-200000000-220000000000000000000000000000000000
χ4944-4-44-4400004-4-400004-400000000000000000000000000000000000000000000000022−2200
χ5044-4-44-4400004-4-400004-4000000000000000000000000000000000000000000000000−222200
χ5144-4-4-44400004-4-40000-440000000000000000000000000000000000000000000000000022−22
χ5244-4-4-44400004-4-40000-4400000000000000000000000000000000000000000000000000−2222
χ534-44-4004004i−4i-44-4000000004i−4i00000000000000000000000000000000000000002-22i−2i0000
χ544-44-4004004i−4i-44-4000000004i−4i0000000000000000000000000000000000000000-22−2i2i0000
χ554-44-400400−4i4i-44-400000000−4i4i00000000000000000000000000000000000000002-2−2i2i0000
χ564-44-400400−4i4i-44-400000000−4i4i0000000000000000000000000000000000000000-222i−2i0000
χ574-4-440044i−4i00-4-440000004i−4i00000000002i−2i2-2002i−2i2i−2i2-22-200000000000000000000000000
χ584-4-440044i−4i00-4-440000004i−4i0000000000−2i2i-2200−2i2i−2i2i-22-2200000000000000000000000000
χ594-4-44004−4i4i00-4-44000000−4i4i00000000002i−2i-22002i−2i2i−2i-22-2200000000000000000000000000
χ604-4-44004−4i4i00-4-44000000−4i4i0000000000−2i2i2-200−2i2i−2i2i2-22-200000000000000000000000000
χ614-4-4400-24i−4i0022-2000000−2i2i00−2i32i323−2300002i−2i2-200−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1−31+3−1+31−300000000000000000000000000
χ624-4-4400-24i−4i0022-2000000−2i2i00−2i32i323−230000−2i2i-2200ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221+3−1−31−3−1+300000000000000000000000000
χ634-4-4400-24i−4i0022-2000000−2i2i002i3−2i3−232300002i−2i2-200ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1+31−3−1−31+300000000000000000000000000
χ644-4-4400-24i−4i0022-2000000−2i2i002i3−2i3−23230000−2i2i-2200−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221−3−1+31+3−1−300000000000000000000000000
χ654-4-4400-2−4i4i0022-20000002i−2i00−2i32i3−232300002i−2i-2200ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221−3−1+31+3−1−300000000000000000000000000
χ664-4-4400-2−4i4i0022-20000002i−2i00−2i32i3−23230000−2i2i2-200−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1+31−3−1−31+300000000000000000000000000
χ674-4-4400-2−4i4i0022-20000002i−2i002i3−2i323−2300002i−2i-2200−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221+3−1−31−3−1+300000000000000000000000000
χ684-4-4400-2−4i4i0022-20000002i−2i002i3−2i323−230000−2i2i2-200ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1−31+3−1+31−300000000000000000000000000
χ6988-8-88-8-40000-4440000-440000000000000000000000000000000000000000000000000000
χ7088-8-8-88-40000-44400004-40000000000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i4-4400000000−4i4i000000000000000000000000000000000000000000000000
χ728-88-800-400−8i8i4-44000000004i−4i000000000000000000000000000000000000000000000000

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