Finite Group Databasebeta

← Group #10698310

Character table — Group #10698310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212444444444466121212121212121212121212121212121212121212121212121244881212121224242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222-2-2-2-22222222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222-2-2-2-22222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222-2-2-2-222-2-2222-2-2-2-22-20000000022-2-22222-2-2-2-20000000000000000000000000000000000002-200
χ122222222-2-2-2-222-2-2222-2-2-2-22-20000000022-2-22222-2-2-2-2000000000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-222222-2-2-2-2-220000000022-2-2-2-2-2-22222000000000000000000000000000000000000002-2
χ142222222-2-2-2-2-2-222222-2-2-2-2-220000000022-2-2-2-2-2-2222200000000000000000000000000000000000000-22
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ20222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ21222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ22222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ232222-2-2222-2-22222222-2-2-2-2-2-200000000-2-22222-2-222-2-20000000000000000002i−2i00002i−2i2i−2i000000000000
χ242222-2-2222-2-22222222-2-2-2-2-2-200000000-2-22222-2-222-2-2000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ252222-2-2222-2-2-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-22200000000000000002-2002-22-20000000000000000
χ262222-2-2222-2-2-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-2220000000000000000-2200-22-220000000000000000
χ272222-2-22-2-22222-2-22222222-2200000000-2-2-2-222-2-2-2-222000000000000000000000000000000002i2i−2i−2i0000
χ282222-2-22-2-22222-2-22222222-2200000000-2-2-2-222-2-2-2-22200000000000000000000000000000000−2i−2i2i2i0000
χ292222-2-22-2-222-2-22222222222-200000000-2-2-2-2-2-22222-2-200000000000000000000000000002i2i−2i−2i00000000
χ302222-2-22-2-222-2-22222222222-200000000-2-2-2-2-2-22222-2-20000000000000000000000000000−2i−2i2i2i00000000
χ312222-2-2-122-2-22222-1-1-11111-2-20000000011-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−3002i−2i−i3i3i3−i3−ii−ii000000000000
χ322222-2-2-122-2-22222-1-1-11111-2-20000000011-1-1-1-111-1-1113333−3−3−3−33333−3−3−3−300−2i2ii3−i3−i3i3i−ii−i000000000000
χ332222-2-2-122-2-22222-1-1-11111-2-20000000011-1-1-1-111-1-111−3−3−3−33333−3−3−3−33333002i−2ii3−i3−i3i3−ii−ii000000000000
χ342222-2-2-122-2-22222-1-1-11111-2-20000000011-1-1-1-111-1-111−3−3−3−33333−3−3−3−3333300−2i2i−i3i3i3−i3i−ii−i000000000000
χ352222-2-2-122-2-2-2-2-2-2-1-1-11111220000000011-1-111-1-111-1-13333−3−3−3−3−3−3−3−333332-200-11-113−3−33000000000000
χ362222-2-2-122-2-2-2-2-2-2-1-1-11111220000000011-1-111-1-111-1-13333−3−3−3−3−3−3−3−33333-22001-11-1−333−3000000000000
χ372222-2-2-122-2-2-2-2-2-2-1-1-11111220000000011-1-111-1-111-1-1−3−3−3−333333333−3−3−3−32-200-11-11−333−3000000000000
χ382222-2-2-122-2-2-2-2-2-2-1-1-11111220000000011-1-111-1-111-1-1−3−3−3−333333333−3−3−3−3-22001-11-13−3−33000000000000
χ3922-2-22-222-2-2200002-2-2-2-2220000002i2i−2i−2i2-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000002−22−2−i2i2−i2i20000
χ4022-2-22-222-2-2200002-2-2-2-2220000002i2i−2i−2i2-22-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000−22−22i2−i2i2−i20000
χ4122-2-22-222-2-2200002-2-2-2-222000000−2i−2i2i2i2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000002−22−2i2−i2i2−i20000
χ4222-2-22-222-2-2200002-2-2-2-222000000−2i−2i2i2i2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000−22−22−i2i2−i2i20000
χ4322-2-2-222-22-2200002-2-2-2-222002i2i−2i−2i0000-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−i2i2i2−i22−2−220000
χ4422-2-2-222-22-2200002-2-2-2-222002i2i−2i−2i0000-22-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000i2−i2−i2i2−222−20000
χ4522-2-2-222-22-2200002-2-2-2-22200−2i−2i2i2i0000-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−i2i2i2−i2−222−20000
χ4622-2-2-222-22-2200002-2-2-2-22200−2i−2i2i2i0000-22-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000i2−i2−i2i22−2−220000
χ47444444-2-4-4-4-444-4-4-2-2-222224-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-444-2-2-22222-4400000000-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ494444-4-4-2-4-44444-4-4-2-2-2-2-2-2-2-44000000002222-2-22222-2-20000000000000000000000000000000000000000
χ504444-4-4-2-4-444-4-444-2-2-2-2-2-2-24-400000000222222-2-2-2-2220000000000000000000000000000000000000000
χ5144-4-44-44-444-400004-4-444-4-400000000004-4-44000000000000000000000000000000000000000000000000
χ5244-4-44-4-24-4-440000-22222-2-20000004i4i−4i−4i-22-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ5344-4-44-4-24-4-440000-22222-2-2000000−4i−4i4i4i-22-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ5444-4-44-4-2-444-40000-222-2-2220000000000-222-200000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000
χ5544-4-44-4-2-444-40000-222-2-2220000000000-222-2000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000
χ5644-4-4-4444-44-400004-4-444-4-40000000000-444-4000000000000000000000000000000000000000000000000
χ5744-4-4-44-24-44-40000-222-2-22200000000002-2-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000
χ5844-4-4-44-24-44-40000-222-2-22200000000002-2-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000
χ5944-4-4-44-2-44-440000-22222-2-2004i4i−4i−4i00002-22-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ6044-4-4-44-2-44-440000-22222-2-200−4i−4i4i4i00002-22-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ614-44-40040000004i−4i-44-40000002-22-22i−2i2i−2i000000004i−4i002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ624-44-40040000004i−4i-44-4000000-22-22−2i2i−2i2i000000004i−4i00-22-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ634-44-4004000000−4i4i-44-40000002-22-2−2i2i−2i2i00000000−4i4i002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ644-44-4004000000−4i4i-44-4000000-22-222i−2i2i−2i00000000−4i4i00-22-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ654-44-400-20000004i−4i2-2223−2323−23002-22-22i−2i2i−2i000000−2i32i3−2i2i00−1+31−3−1+31−3−1−31+3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ664-44-400-20000004i−4i2-2223−2323−2300-22-22−2i2i−2i2i000000−2i32i3−2i2i001−3−1+31−3−1+31+3−1−31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ674-44-400-20000004i−4i2-22−2323−2323002-22-22i−2i2i−2i0000002i3−2i3−2i2i00−1−31+3−1−31+3−1+31−3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ684-44-400-20000004i−4i2-22−2323−232300-22-22−2i2i−2i2i0000002i3−2i3−2i2i001+3−1−31+3−1−31−3−1+31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ694-44-400-2000000−4i4i2-2223−2323−23002-22-2−2i2i−2i2i0000002i3−2i32i−2i00−1+31−3−1+31−3−1−31+3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ704-44-400-2000000−4i4i2-2223−2323−2300-22-222i−2i2i−2i0000002i3−2i32i−2i001−3−1+31−3−1+31+3−1−31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ714-44-400-2000000−4i4i2-22−2323−2323002-22-2−2i2i−2i2i000000−2i32i32i−2i00−1−31+3−1−31+3−1+31−3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ724-44-400-2000000−4i4i2-22−2323−232300-22-222i−2i2i−2i000000−2i32i32i−2i001+3−1−31+3−1−31−3−1+31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ734-4-4400400004i−4i00-4-440000002i−2i−2i2i2-2-2200004i−4i0000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000
χ744-4-4400400004i−4i00-4-44000000−2i2i2i−2i-222-200004i−4i000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000
χ754-4-440040000−4i4i00-4-440000002i−2i−2i2i-222-20000−4i4i0000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000
χ764-4-440040000−4i4i00-4-44000000−2i2i2i−2i2-2-220000−4i4i000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000
χ774-4-4400-200004i−4i0022-223−23−2323002i−2i−2i2i2-2-220000−2i2i0000−2i32i3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ784-4-4400-200004i−4i0022-223−23−232300−2i2i2i−2i-222-20000−2i2i0000−2i32i3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ794-4-4400-200004i−4i0022-2−232323−23002i−2i−2i2i2-2-220000−2i2i00002i3−2i3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000
χ804-4-4400-200004i−4i0022-2−232323−2300−2i2i2i−2i-222-20000−2i2i00002i3−2i3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ814-4-4400-20000−4i4i0022-223−23−2323002i−2i−2i2i-222-200002i−2i00002i3−2i3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ824-4-4400-20000−4i4i0022-223−23−232300−2i2i2i−2i2-2-2200002i−2i00002i3−2i3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ834-4-4400-20000−4i4i0022-2−232323−23002i−2i−2i2i-222-200002i−2i0000−2i32i3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ844-4-4400-20000−4i4i0022-2−232323−2300−2i2i2i−2i2-2-2200002i−2i0000−2i32i3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000

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