Finite Group Databasebeta

← Group #10772154

Character table — Group #10772154

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881616161616162424242424242424242424244848
order1222344444466612121212244444441212121212121212246668888121212121212122424242424242424882424242422244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-111-1-1111111111-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-111
χ61111111111111111111-1-111-1-1111111111-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111111-1-1
χ71111111111111111111-1-111-1-1111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-11111-1-1
χ81111111111111111111-1-111-1-1111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-11-1-1-1-111
χ9111111-1-11111111111-111-1-1-1-1111-1-1-1-111-11-1-1-111-1-1-11111-1-11111-1-1-1-11-111-1-11111-1-1-1-111-1-11-1
χ10111111-1-11111111111-111-1-1-1-1111-1-1-1-111-11-1-1-111-1-1-11111-1-11111-1-1-1-11-111-1-1-1-1-1-11111-1-111-11
χ11111111-1-11111111111-111-1-1-1-1111-1-1-1-111-11-1-1-1-1-111-11111-1-1-1-1-1-11111-11-1-1111111-1-1-1-1-1-111-11
χ12111111-1-11111111111-111-1-1-1-1111-1-1-1-111-11-1-1-1-1-111-11111-1-1-1-1-1-11111-11-1-111-1-1-1-1111111-1-11-1
χ13111111-1-11111111111-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-11-1-11-1-1111-1
χ14111111-1-11111111111-1-1-1-1-111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-111-111-111-1-1-11
χ15111111-1-11111111111-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-1-1-111-1-1-1-111111-111-1-111-1-11-1-1111-1-1-11
χ16111111-1-11111111111-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-111-1-1-1111-1
χ1722222222-2-22222-2-2-2-2222-2-2-2-2-22222-2-2-2-22-22220000-222-2-2-2-20000000000000000000000000000
χ1822222222-2-22222-2-2-2-22-2-2-2-222-22222-2-2-2-2-222-2-20000-2-2-222220000000000000000000000000000
χ19222222-2-2-2-22222-2-2-2-2-2222222-222-2-222-2-2-2-2-2-2-20000222-2-2220000000000000000000000000000
χ20222222-2-2-2-22222-2-2-2-2-2-2-222-2-2-222-2-222-2-222-22200002-2-222-2-20000000000000000000000000000
χ2122222-22222-22222222-2002-200-2-2-22222-2-200-2000000-200000000000000000000002-2-2002000000
χ2222222-22222-22222222-2002-200-2-2-22222-2-200-2000000-20000000000000000000000-22200-2000000
χ2322222-222-2-2-2222-2-2-2-2-200-22002-2-222-2-22200-20000002000000000000000000002-20002-20000000
χ2422222-222-2-2-2222-2-2-2-2-200-22002-2-222-2-22200-2000000200000000000000000000-22000-220000000
χ2522222-2-2-222-22222222200-2200-2-2-2-2-2-2-2-2-2002000000200000000000000000000002-2200-2000000
χ2622222-2-2-222-22222222200-2200-2-2-2-2-2-2-2-2-200200000020000000000000000000000-22-2002000000
χ2722222-2-2-2-2-2-2222-2-2-2-22002-2002-2-2-2-22222002000000-2000000000000000000002-2000-220000000
χ2822222-2-2-2-2-2-2222-2-2-2-22002-2002-2-2-2-22222002000000-200000000000000000000-220002-20000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2111100000000000000
χ312222-1222222-1-1-1-1-1-1-12-2-222-2-22-1-1-1-1-1-1-1-1-2-2-1112222-1111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ322222-1222222-1-1-1-1-1-1-12-2-222-2-22-1-1-1-1-1-1-1-1-2-2-111-2-2-2-2-11111111111111122-1-1-1-100000000000000
χ332222-1222-2-22-1-1-11111222-2-2-2-2-2-1-1-1-111112-2-1-1-100001-1-1111133−3−333−3−3003−33−300000000000000
χ342222-1222-2-22-1-1-11111222-2-2-2-2-2-1-1-1-111112-2-1-1-100001-1-11111−3−333−3−33300−33−3300000000000000
χ352222-1222-2-22-1-1-111112-2-2-2-222-2-1-1-1-11111-22-1110000111-1-1-1-133−3−333−3−300−33−3300000000000000
χ362222-1222-2-22-1-1-111112-2-2-2-222-2-1-1-1-11111-22-1110000111-1-1-1-1−3−333−3−333003−33−300000000000000
χ372222-12-2-2222-1-1-1-1-1-1-1-222-2-2-2-22-1-11111-1-1-2211122-2-21-1-1-1-111-1-1-1-111112-2-1-11100000000000000
χ382222-12-2-2222-1-1-1-1-1-1-1-222-2-2-2-22-1-11111-1-1-22111-2-2221-1-1-1-1111111-1-1-1-1-2211-1-100000000000000
χ392222-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2222-1-11111-1-12-21-1-122-2-211111-1-1-1-1-1-11111-2211-1-100000000000000
χ402222-12-2-2222-1-1-1-1-1-1-1-2-2-2-2-2222-1-11111-1-12-21-1-1-2-22211111-1-11111-1-1-1-12-2-1-11100000000000000
χ412222-12-2-2-2-22-1-1-11111-2222222-2-1-111-1-111-2-21110000-1-1-111-1-133−3−3−3−333003−3−3300000000000000
χ422222-12-2-2-2-22-1-1-11111-2222222-2-1-111-1-111-2-21110000-1-1-111-1-1−3−33333−3−300−333−300000000000000
χ432222-12-2-2-2-22-1-1-11111-2-2-222-2-2-2-1-111-1-111221-1-10000-111-1-11133−3−3−3−33300−333−300000000000000
χ442222-12-2-2-2-22-1-1-11111-2-2-222-2-2-2-1-111-1-111221-1-10000-111-1-111−3−33333−3−3003−3−3300000000000000
χ454444-2-44444-4-2-2-2-2-2-2-2-4004-400-422-2-2-2-22200200000020000000000000000000000000000000000
χ464444-2-444-4-4-4-2-2-22222-400-4400422-2-222-2-2002000000-20000000000000000000000000000000000
χ474444-2-4-4-444-4-2-2-2-2-2-2-2400-4400-42222222200-2000000-20000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-222224004-40042222-2-2-2-200-200000020000000000000000000000000000000000
χ4944-4-4440000-44-4-4000004-4000004-400000000000000004-400000000000000000000000000000000
χ5044-4-4440000-44-4-400000-44000004-40000000000000000-4400000000000000000000000000000000
χ5144-4-44-4000044-4-40000000004i−4i0-44000000000000000000004i−4i0000000000000000000000000000
χ5244-4-44-4000044-4-4000000000−4i4i0-4400000000000000000000−4i4i0000000000000000000000000000
χ5344-4-4-240000-4-22223−2323−2304-400000-22000023−230000000000-2223−23000000000000000000000000000000
χ5444-4-4-240000-4-22223−2323−230-4400000-22000023−2300000000002-2−2323000000000000000000000000000000
χ5544-4-4-240000-4-222−2323−232304-400000-220000−23230000000000-22−2323000000000000000000000000000000
χ5644-4-4-240000-4-222−2323−23230-4400000-220000−232300000000002-223−23000000000000000000000000000000
χ5744-4-4-2-400004-22223−2323−23000004i−4i02-20000−2323000−2i32i3000000000−2i2i0000000000000000000000000000
χ5844-4-4-2-400004-22223−2323−2300000−4i4i02-20000−23230002i3−2i30000000002i−2i0000000000000000000000000000
χ5944-4-4-2-400004-222−2323−2323000004i−4i02-2000023−230002i3−2i3000000000−2i2i0000000000000000000000000000
χ6044-4-4-2-400004-222−2323−232300000−4i4i02-2000023−23000−2i32i30000000002i−2i0000000000000000000000000000
χ614-44-4404i−4i000-44-4000000000000004i−4i0000000002-22i−2i00000002-22-22i−2i2i−2i00000000000000000000
χ624-44-4404i−4i000-44-4000000000000004i−4i000000000-22−2i2i0000000-22-22−2i2i−2i2i00000000000000000000
χ634-44-440−4i4i000-44-400000000000000−4i4i0000000002-2−2i2i00000002-22-2−2i2i−2i2i00000000000000000000
χ644-44-440−4i4i000-44-400000000000000−4i4i000000000-222i−2i0000000-22-222i−2i2i−2i00000000000000000000
χ654-44-4-204i−4i0002-2223−23−23230000000000−2i2i−2i32i300000002-22i−2i0000000−1−31+3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ664-44-4-204i−4i0002-2223−23−23230000000000−2i2i−2i32i30000000-22−2i2i00000001+3−1−31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ674-44-4-204i−4i0002-22−232323−230000000000−2i2i2i3−2i300000002-22i−2i0000000−1+31−3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ684-44-4-204i−4i0002-22−232323−230000000000−2i2i2i3−2i30000000-22−2i2i00000001−3−1+31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ694-44-4-20−4i4i0002-2223−23−232300000000002i−2i2i3−2i300000002-2−2i2i0000000−1−31+3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ704-44-4-20−4i4i0002-2223−23−232300000000002i−2i2i3−2i30000000-222i−2i00000001+3−1−31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ714-44-4-20−4i4i0002-22−232323−2300000000002i−2i−2i32i300000002-2−2i2i0000000−1+31−3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ724-44-4-20−4i4i0002-22−232323−2300000000002i−2i−2i32i30000000-222i−2i00000001−3−1+31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ734-4-4440004-40-4-4444-4-400000000000000000000000000000000000000000000000000000000−2i22i200
χ744-4-4440004-40-4-4444-4-4000000000000000000000000000000000000000000000000000000002i2−2i200
χ754-4-444000-440-4-44-4-44400000000000000000000000000000000000000000000000000000022−220000
χ764-4-444000-440-4-44-4-444000000000000000000000000000000000000000000000000000000−22220000
χ778-8-88-40008-8044-4-4-444000000000000000000000000000000000000000000000000000000000000
χ788-8-88-4000-88044-444-4-4000000000000000000000000000000000000000000000000000000000000

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