Finite Group Databasebeta

← Group #10692501

Character table — Group #10692501

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222222223446666666444666688888888121212124444121212121212121212122424242424242424224444448888888844121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111-1-11-1-11-1-111-1-11-1-111-11-1-11iiii−i−i−i−i11-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ1011111-1-11-1-11-1-111-1-11-1-111-11-1-11iiii−i−i−i−i11-1-111-1-11-11111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiii−iii−i−i-11−ii
χ1111111-1-11-1-11-1-111-1-11-1-111-11-1-11iiii−i−i−i−i11-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ1211111-1-11-1-11-1-111-1-11-1-111-11-1-11iiii−i−i−i−i11-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−ii−i−iii1-1i−i
χ1311111-1-11-1-11-1-111-1-11-1-111-11-1-11−i−i−i−iiiii11-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ1411111-1-11-1-11-1-111-1-11-1-111-11-1-11−i−i−i−iiiii11-1-111-1-11-11111-1-1-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−ii−i−iii-11i−i
χ1511111-1-11-1-11-1-111-1-11-1-111-11-1-11−i−i−i−iiiii11-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ1611111-1-11-1-11-1-111-1-11-1-111-11-1-11−i−i−i−iiiii11-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−ii−iii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-2222200000000-2-2-2-20000-2-200000000000000002222-2-2-2-2000000000000000000
χ1822222222222-2-22222222-2-2-2222200000000-2-2-2-20000-2-20000000000000000-2-2-2-22222000000000000000000
χ192222222222-122-1-1-1-1-1-1-1222-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ202222222222-122-1-1-1-1-1-1-1222-1-1-1-122222222-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ212222222222-122-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ222222222222-122-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ2322222-2-22-2-222222-2-22-2-2-2-222-2-2200000000-2-2220000-22000000000000000022-2-2-2-222000000000000000000
χ2422222-2-22-2-222222-2-22-2-2-2-222-2-2200000000-2-2220000-220000000000000000-2-22222-2-2000000000000000000
χ2522222-2-22-2-2-1-2-2-1-111-11122-2-111-12i2i2i2i−2i−2i−2i−2i-1-11122-2-2-11-1-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ2622222-2-22-2-2-1-2-2-1-111-11122-2-111-12i2i2i2i−2i−2i−2i−2i-1-111-2-222-111111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ2722222-2-22-2-2-1-2-2-1-111-11122-2-111-1−2i−2i−2i−2i2i2i2i2i-1-11122-2-2-11-1-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ2822222-2-22-2-2-1-2-2-1-111-11122-2-111-1−2i−2i−2i−2i2i2i2i2i-1-111-2-222-111111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-22-2-22-222222222222-2-2-2-2-2-20000000022220000-2-200000000000000000000000022-2-222-2-20000000000
χ302222-22-2-22-222222222222-2-2-2-2-2-20000000022220000-2-2000000000000000000000000-2-222-2-2220000000000
χ312222-22-2-22-22-2-22222222-222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2000022000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ322222-22-2-22-22-2-22222222-222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-200002200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ332222-22-2-22-2-1-2-2-1-1-1-1-1-1-1-22211112i2i−2i−2i2i2i−2i−2i11110000-1-133−3−333−3−3−i−iii−i−iii000000000000000000−i3i3−i3i30000
χ342222-22-2-22-2-1-2-2-1-1-1-1-1-1-1-22211112i2i−2i−2i2i2i−2i−2i11110000-1-1−3−333−3−333−i−iii−i−iii000000000000000000i3−i3i3−i30000
χ352222-22-2-22-2-1-2-2-1-1-1-1-1-1-1-2221111−2i−2i2i2i−2i−2i2i2i11110000-1-133−3−333−3−3ii−i−iii−i−i000000000000000000i3−i3i3−i30000
χ362222-22-2-22-2-1-2-2-1-1-1-1-1-1-1-2221111−2i−2i2i2i−2i−2i2i2i11110000-1-1−3−333−3−333ii−i−iii−i−i000000000000000000−i3i3−i3i30000
χ372222-2-22-2-2222222-2-22-2-2-22-2-222-222-2-2-2-222-2-22200002-20000000022-2-2-2-22200000000000000000000000000
χ382222-2-22-2-2222222-2-22-2-2-22-2-222-2-2-22222-2-2-2-22200002-200000000-2-22222-2-200000000000000000000000000
χ392222-2-22-2-222-2-222-2-22-2-22-22-222-20000000022-2-20000-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ402222-2-22-2-222-2-222-2-22-2-22-22-222-20000000022-2-20000-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ412222-2-22-2-22-122-1-111-111-22-21-1-1122-2-2-2-22211-1-10000-1133−3−3−3−333-1-11111-1-1000000000000000000−333−30000
χ422222-2-22-2-22-122-1-111-111-22-21-1-1122-2-2-2-22211-1-10000-11−3−33333−3−3-1-11111-1-10000000000000000003−3−330000
χ432222-2-22-2-22-122-1-111-111-22-21-1-11-2-22222-2-211-1-10000-1133−3−3−3−33311-1-1-1-1110000000000000000003−3−330000
χ442222-2-22-2-22-122-1-111-111-22-21-1-11-2-22222-2-211-1-10000-11−3−33333−3−311-1-1-1-111000000000000000000−333−30000
χ4522-2-2222-2-2-22002-222-2-2-200022-2-22−22−22−22−20000000000000000002−22−22−22−22-22-200002−22−22−22−20000000000
χ4622-2-2222-2-2-22002-222-2-2-200022-2-22−22−22−22−20000000000000000002−22−22−22−2-22-220000−22−22−22−220000000000
χ4722-2-2222-2-2-22002-222-2-2-200022-2-2−22−22−22−22000000000000000000−22−22−22−222-22-20000−22−22−22−220000000000
χ4822-2-2222-2-2-22002-222-2-2-200022-2-2−22−22−22−22000000000000000000−22−22−22−22-22-2200002−22−22−22−20000000000
χ4922-2-22-2-2-2222002-2-2-2-2220002-22-2−i2i2−i2i2i2−i2i2−i2000000000000000000−i2i2−i2i2i2−i2i2−i22-2-220000−i2i2−i2i2i2−i2i2−i20000000000
χ5022-2-22-2-2-2222002-2-2-2-2220002-22-2−i2i2−i2i2i2−i2i2−i2000000000000000000−i2i2−i2i2i2−i2i2−i2-222-20000i2−i2i2−i2−i2i2−i2i20000000000
χ5122-2-22-2-2-2222002-2-2-2-2220002-22-2i2−i2i2−i2−i2i2−i2i2000000000000000000i2−i2i2−i2−i2i2−i2i22-2-220000i2−i2i2−i2−i2i2−i2i20000000000
χ5222-2-22-2-2-2222002-2-2-2-2220002-22-2i2−i2i2−i2−i2i2−i2i2000000000000000000i2−i2i2−i2−i2i2−i2i2-222-20000−i2i2−i2i2i2−i2i2−i20000000000
χ5322-2-2-22-22-222002-222-2-2-2000-2-222−i2i2i2−i2−i2i2i2−i2000000000000000000−i2i2i2−i2−i2i2i2−i200002i−2i2i−2i2−2−222−2−220000000000
χ5422-2-2-22-22-222002-222-2-2-2000-2-222−i2i2i2−i2−i2i2i2−i2000000000000000000−i2i2i2−i2−i2i2i2−i20000−2i2i−2i2i−222−2−222−20000000000
χ5522-2-2-22-22-222002-222-2-2-2000-2-222i2−i2−i2i2i2−i2−i2i2000000000000000000i2−i2−i2i2i2−i2−i2i200002i−2i2i−2i−222−2−222−20000000000
χ5622-2-2-22-22-222002-222-2-2-2000-2-222i2−i2−i2i2i2−i2−i2i2000000000000000000i2−i2−i2i2i2−i2−i2i20000−2i2i−2i2i2−2−222−2−220000000000
χ5722-2-2-2-2222-22002-2-2-2-222000-22-222−2−22−222−20000000000000000002−2−22−222−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000
χ5822-2-2-2-2222-22002-2-2-2-222000-22-222−2−22−222−20000000000000000002−2−22−222−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000
χ5922-2-2-2-2222-22002-2-2-2-222000-22-22−222−22−2−22000000000000000000−222−22−2−2200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000
χ6022-2-2-2-2222-22002-2-2-2-222000-22-22−222−22−2−22000000000000000000−222−22−2−220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000
χ614444444444-2-4-4-2-2-2-2-2-2-2-4-4-4-2-2-2-2000000002222000022000000000000000000000000000000000000000000
χ6244444-4-44-4-4-244-2-222-222-4-44-222-20000000022-2-200002-2000000000000000000000000000000000000000000
χ634444-44-4-44-4-244-2-2-2-2-2-2-24-4-4222200000000-2-2-2-2000022000000000000000000000000000000000000000000
χ644444-4-44-4-44-2-4-4-2-222-2224-442-2-2200000000-2-22200002-2000000000000000000000000000000000000000000
χ6544-4-4444-4-4-4-200-22-2-2222000-2-22222−2222−2222−2222−22000000000000000000−22−22−22−2200000000000000000000000000
χ6644-4-4444-4-4-4-200-22-2-2222000-2-222−2222−2222−2222−22220000000000000000002−22−22−22−200000000000000000000000000
χ6744-4-44-4-4-444-200-22222-2-2000-22-22−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ6844-4-44-4-4-444-200-22222-2-2000-22-222i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ6944-4-4-44-44-44-200-22-2-222200022-2-2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ7044-4-4-44-44-44-200-22-2-222200022-2-22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ7144-4-4-4-4444-4-200-22222-2-20002-22-222−22−2222−222222−22000000000000000000−222−22−2−2200000000000000000000000000
χ7244-4-4-4-4444-4-200-22222-2-20002-22-2−222222−2222−22−22220000000000000000002−2−22−222−200000000000000000000000000
χ734-44-400000044i−4i-4400-400000000000000000004i−4i2-22i−2i002-22-22i−2i2i−2i0000000000000000000000000000000000
χ744-44-400000044i−4i-4400-400000000000000000004i−4i-22−2i2i00-22-22−2i2i−2i2i0000000000000000000000000000000000
χ754-44-40000004−4i4i-4400-40000000000000000000−4i4i2-2−2i2i002-22-2−2i2i−2i2i0000000000000000000000000000000000
χ764-44-40000004−4i4i-4400-40000000000000000000−4i4i-222i−2i00-22-222i−2i2i−2i0000000000000000000000000000000000
χ774-44-4000000-24i−4i2-2−2i32i32−2i32i300000000000000023−23−2i2i2-22i−2i00−1+31−3−1−31+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000000000
χ784-44-4000000-24i−4i2-2−2i32i32−2i32i300000000000000023−23−2i2i-22−2i2i001−3−1+31+3−1−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000000000
χ794-44-4000000-24i−4i2-22i3−2i322i3−2i3000000000000000−2323−2i2i2-22i−2i00−1−31+3−1+31−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000000000
χ804-44-4000000-24i−4i2-22i3−2i322i3−2i3000000000000000−2323−2i2i-22−2i2i001+3−1−31−3−1+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000000000
χ814-44-4000000-2−4i4i2-2−2i32i32−2i32i3000000000000000−23232i−2i2-2−2i2i00−1−31+3−1+31−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000000000
χ824-44-4000000-2−4i4i2-2−2i32i32−2i32i3000000000000000−23232i−2i-222i−2i001+3−1−31−3−1+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000000000
χ834-44-4000000-2−4i4i2-22i3−2i322i3−2i300000000000000023−232i−2i2-2−2i2i00−1+31−3−1−31+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000000000
χ844-44-4000000-2−4i4i2-22i3−2i322i3−2i300000000000000023−232i−2i-222i−2i001−3−1+31+3−1−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000000000
χ858-8-88000000800-8-8008000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88000000-40044−4i34i3-44i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88000000-400444i3−4i3-4−4i34i30000000000000000000000000000000000000000000000000000000000000000000

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