Finite Group Databasebeta

← Group #10698913

Character table — Group #10698913

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242444881212121224242424444488888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222-2-2-22-2222-2-2-2-2-2-22200000000-2-22222-2-2-2-20000000000000000002i−2i00002i2i−2i−2i000000000000
χ102222222222-2-2-22-2222-2-2-2-2-2-22200000000-2-22222-2-2-2-2000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ112222222-2-2-2222-222222222-2-2220000000022-2-2-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ122222222-2-2-2222-222222222-2-2220000000022-2-2-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ132222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i
χ15222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1222-2-2-22-2-1-1-11111-2-2-1-10000000011-1-1-1-1111133333333−3−3−3−3−3−3−3−3002i−2i−i3−i3i3i3−i−iii000000000000
χ20222222-1222-2-2-22-2-1-1-11111-2-2-1-10000000011-1-1-1-1111133333333−3−3−3−3−3−3−3−300−2i2ii3i3−i3−i3ii−i−i000000000000
χ21222222-1222-2-2-22-2-1-1-11111-2-2-1-10000000011-1-1-1-11111−3−3−3−3−3−3−3−333333333002i−2ii3i3−i3−i3−i−iii000000000000
χ22222222-1222-2-2-22-2-1-1-11111-2-2-1-10000000011-1-1-1-11111−3−3−3−3−3−3−3−33333333300−2i2i−i3−i3i3i3ii−i−i000000000000
χ232222-2-2222-22-22-2-222222222-2-2-200000000-2-222-2-222-2-2000000000000000000000000000000002i2i−2i−2i0000
χ242222-2-2222-22-22-2-222222222-2-2-200000000-2-222-2-222-2-200000000000000000000000000000000−2i−2i2i2i0000
χ252222-2-2222-2-22-2-22222-2-2-2-2-22-2-2000000002222-2-2-2-2220000000000000000000000000000000000002-200
χ262222-2-2222-2-22-2-22222-2-2-2-2-22-2-2000000002222-2-2-2-222000000000000000000000000000000000000-2200
χ272222-2-22-2-222-222-22222222-22-2-22222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ282222-2-22-2-222-222-22222222-22-2-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ292222-2-22-2-22-22-222222-2-2-2-22-2-2-20000000022-2-22222-2-200000000000000002-2002-22-20000000000000000
χ302222-2-22-2-22-22-222222-2-2-2-22-2-2-20000000022-2-22222-2-20000000000000000-2200-22-220000000000000000
χ312222-2-2-1-2-222-222-2-1-1-1-1-1-1-1-22112222-2-2-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3i3−i3−i3i3−i3i3000000000000
χ322222-2-2-1-2-222-222-2-1-1-1-1-1-1-1-22112222-2-2-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3−i3i3i3−i3i3−i3000000000000
χ332222-2-2-1-2-222-222-2-1-1-1-1-1-1-1-2211-2-2-2-222221111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3i3−i3000000000000
χ342222-2-2-1-2-222-222-2-1-1-1-1-1-1-1-2211-2-2-2-222221111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3−i3i3000000000000
χ352222-2-2-1-2-22-22-222-1-1-111112-21100000000-1-111-1-1-1-1113333−3−3−3−3−3−3−3−333332-200-11-113−3−33000000000000
χ362222-2-2-1-2-22-22-222-1-1-111112-21100000000-1-111-1-1-1-1113333−3−3−3−3−3−3−3−33333-22001-11-1−333−3000000000000
χ372222-2-2-1-2-22-22-222-1-1-111112-21100000000-1-111-1-1-1-111−3−3−3−333333333−3−3−3−32-200-11-11−333−3000000000000
χ382222-2-2-1-2-22-22-222-1-1-111112-21100000000-1-111-1-1-1-111−3−3−3−333333333−3−3−3−3-22001-11-13−3−33000000000000
χ392-22-22-2200022-20-22-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−20000000000002-2002−22−20000
χ402-22-22-2200022-20-22-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−2000000000000-2200−22−220000
χ412-22-22-2200022-20-22-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−2220000000000002-200−22−220000
χ422-22-22-2200022-20-22-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−222000000000000-22002−22−20000
χ432-22-2-2220002-2-2022-2-222-2-200-2222−2−2−2−222-220000000022−2−2−2−22222−2−2−2−222000000000000002i−2i−i2i2i2−i20000
χ442-22-2-2220002-2-2022-2-222-2-200-2222−2−2−2−222-220000000022−2−2−2−22222−2−2−2−22200000000000000−2i2ii2−i2−i2i20000
χ452-22-2-2220002-2-2022-2-222-2-200-22−2−22222−2−2-2200000000−2−22222−2−2−2−22222−2−2000000000000002i−2ii2−i2−i2i20000
χ462-22-2-2220002-2-2022-2-222-2-200-22−2−22222−2−2-2200000000−2−22222−2−2−2−22222−2−200000000000000−2i2i−i2i2i2−i20000
χ47444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4-2-200000000-2-2222222220000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-2222244-2-200000000222222-2-2-2-20000000000000000000000000000000000000000
χ494444-4-4-244-44-44-4-4-2-2-2-2-2-2-24-4220000000022-2-222-2-2220000000000000000000000000000000000000000
χ504444-4-4-244-4-44-4-44-2-2-22222-442200000000-2-2-2-22222-2-20000000000000000000000000000000000000000
χ5144-4-4004004000-40-44-400000000000022−2222−2200004-40000000022−2222−22000022−2222−22000000000000000000000000
χ5244-4-4004004000-40-44-4000000000000−2222−222200004-400000000−2222−22220000−2222−2222000000000000000000000000
χ5344-4-400400-400040-44-400000000−2i22i2−2i22i200000000-440000−2i22i2−2i22i20000−2i22i2−2i22i20000000000000000000000000000
χ5444-4-400400-400040-44-4000000002i2−2i22i2−2i200000000-4400002i2−2i22i2−2i200002i2−2i22i2−2i20000000000000000000000000000
χ5544-4-400-2004000-402-2223−2323−230000000022−2222−220000-220023−2300002ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ2300002ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ5644-4-400-2004000-402-2223−2323−2300000000−2222−22220000-220023−230000−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ230000−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ5744-4-400-2004000-402-22−2323−23230000000022−2222−220000-2200−232300002ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ700002ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ5844-4-400-2004000-402-22−2323−232300000000−2222−22220000-2200−23230000−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ70000−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ5944-4-400-200-4000402-2223−2323−230000−2i22i2−2i22i2000000002-200−23232ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ700002ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000
χ6044-4-400-200-4000402-2223−2323−2300002i2−2i22i2−2i2000000002-200−2323−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ70000−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000
χ6144-4-400-200-4000402-22−2323−23230000−2i22i2−2i22i2000000002-20023−232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ2300002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ6244-4-400-200-4000402-22−2323−232300002i2−2i22i2−2i2000000002-20023−23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ230000−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000
χ634-44-44-44000-4-44044-4-4-4-444004-400000000-44000000000000000000000000000000000000000000000000
χ644-44-44-4-200044-40-4-222-2-22200-222222−22−222222−22−22-2200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ654-44-44-4-200044-40-4-222-2-22200-22−22−222222−22−222222-220000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ664-44-44-4-2000-4-4404-22222-2-200-22000000002-20000000066−6−666−6−6−6−666−6−666000000000000000000000000
χ674-44-44-4-2000-4-4404-22222-2-200-22000000002-200000000−6−666−6−66666−6−666−6−6000000000000000000000000
χ684-44-4-444000-4440-44-4-4-4-44400-44000000004-4000000000000000000000000000000000000000000000000
χ694-44-4-44-20004-4-404-222-2-222002-22222−22−22−22−2222222-200000000−2−22222−2−2−2−22222−2−2000000000000000000000000
χ704-44-4-44-20004-4-404-222-2-222002-2−22−2222222222−22−222-20000000022−2−2−2−22222−2−2−2−222000000000000000000000000
χ714-44-4-44-2000-4440-4-22222-2-2002-200000000-220000000066−6−6−6−666−6−66666−6−6000000000000000000000000
χ724-44-4-44-2000-4440-4-22222-2-2002-200000000-2200000000−6−66666−6−666−6−6−6−666000000000000000000000000
χ734-4-440044i−4i000000-4-44000000002i−2i−2i2i2-2-22004i−4i0000002i−2i−2i2i2-2-222i−2i−2i2i2-2-22000000000000000000000000
χ744-4-440044i−4i000000-4-4400000000−2i2i2i−2i-222-2004i−4i000000−2i2i2i−2i-222-2−2i2i2i−2i-222-2000000000000000000000000
χ754-4-44004−4i4i000000-4-44000000002i−2i−2i2i-222-200−4i4i0000002i−2i−2i2i-222-22i−2i−2i2i-222-2000000000000000000000000
χ764-4-44004−4i4i000000-4-4400000000−2i2i2i−2i2-2-2200−4i4i000000−2i2i2i−2i2-2-22−2i2i2i−2i2-2-22000000000000000000000000
χ774-4-4400-24i−4i00000022-223−23−232300002i−2i−2i2i2-2-2200−2i2i00−2i32i300−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1−31+31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1+31−31−3−1+3000000000000000000000000
χ784-4-4400-24i−4i00000022-223−23−23230000−2i2i2i−2i-222-200−2i2i00−2i32i300ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221+3−1−3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221−3−1+3−1+31−3000000000000000000000000
χ794-4-4400-24i−4i00000022-2−232323−2300002i−2i−2i2i2-2-2200−2i2i002i3−2i300ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1+31−31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1−31+31+3−1−3000000000000000000000000
χ804-4-4400-24i−4i00000022-2−232323−230000−2i2i2i−2i-222-200−2i2i002i3−2i300−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221−3−1+3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221+3−1−3−1−31+3000000000000000000000000
χ814-4-4400-2−4i4i00000022-223−23−232300002i−2i−2i2i-222-2002i−2i002i3−2i300−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221+3−1−3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221−3−1+3−1+31−3000000000000000000000000
χ824-4-4400-2−4i4i00000022-223−23−23230000−2i2i2i−2i2-2-22002i−2i002i3−2i300ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1−31+31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1+31−31−3−1+3000000000000000000000000
χ834-4-4400-2−4i4i00000022-2−232323−2300002i−2i−2i2i-222-2002i−2i00−2i32i300ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221−3−1+3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221+3−1−3−1−31+3000000000000000000000000
χ844-4-4400-2−4i4i00000022-2−232323−230000−2i2i2i−2i2-2-22002i−2i00−2i32i300−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1+31−31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1−31+31+3−1−3000000000000000000000000

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