Finite Group Databasebeta

← Group #10692432

Character table — Group #10692432

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888888888888888888888888888824242424484848484848
order12223444466612121212244448888121212122424242424242424224466666888888121212121212122424242424242424242424248888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ8111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ911111-1-1-1-1111-1-1-1-1-111-11ii−i−i11-1-1iiii−i−i−i−i1-11-1-111-1-1i−iii−i−i1-1111-1-1ii−i−iiiii−i−i−i−iii−i−i1-1i−i1-1
χ1011111-1-1-1-1111-1-1-1-1-111-11ii−i−i11-1-1iiii−i−i−i−i1-11-1-111-1-1i−iii−i−i1-1111-1-1ii−i−iiiii−i−i−i−i−i−iii-11−ii-11
χ1111111-1-1-1-1111-1-1-1-1-111-11ii−i−i11-1-1iiii−i−i−i−i-11-11-1-1-111i−i−i−iii1-11-1-111ii−i−i−i−i−i−iiiiiii−i−i1-1−ii-11
χ1211111-1-1-1-1111-1-1-1-1-111-11ii−i−i11-1-1iiii−i−i−i−i-11-11-1-1-111i−i−i−iii1-11-1-111ii−i−i−i−i−i−iiiii−i−iii-11i−i1-1
χ1311111-1-1-1-1111-1-1-1-1-111-11−i−iii11-1-1−i−i−i−iiiii1-11-1-111-1-1−ii−i−iii1-1111-1-1−i−iii−i−i−i−iiiiiii−i−i-11i−i-11
χ1411111-1-1-1-1111-1-1-1-1-111-11−i−iii11-1-1−i−i−i−iiiii1-11-1-111-1-1−ii−i−iii1-1111-1-1−i−iii−i−i−i−iiiii−i−iii1-1−ii1-1
χ1511111-1-1-1-1111-1-1-1-1-111-11−i−iii11-1-1−i−i−i−iiiii-11-11-1-1-111−iiii−i−i1-11-1-111−i−iiiiiii−i−i−i−iii−i−i-11−ii1-1
χ1611111-1-1-1-1111-1-1-1-1-111-11−i−iii11-1-1−i−i−i−iiiii-11-11-1-1-111−iiii−i−i1-11-1-111−i−iiiiiii−i−i−i−i−i−iii1-1i−i-11
χ172222222222222222-2-22-2-222222222222222220000-20000-2-20000-2-2-20000-2-2-2-2000000000000000000
χ182222222222222222-2-22-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000-20000220000-2-2-200002222000000000000000000
χ19222222-2-22222-2-2-2-222-2-2-20000-2-22200000000000020000002i−2i2i−2i2-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000
χ20222222-2-22222-2-2-2-222-2-2-20000-2-2220000000000002000000−2i2i−2i2i2-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000
χ21222222-2-22222-2-2-2-2-2-2-2220000-2-2220000000022-2-2-22222000000-222-2-2-2-20000000000000000000000
χ22222222-2-22222-2-2-2-2-2-2-2220000-2-22200000000-2-222-2-2-2-2-2000000-22222220000000000000000000000
χ2322222-222-222222222-2-2-220000-2-2-2-2000000002-2-22222-2-2000000-2-22-2-2220000000000000000000000
χ2422222-222-222222222-2-2-220000-2-2-2-200000000-222-22-2-222000000-2-2222-2-20000000000000000000000
χ2522222-222-22222222-22-22-20000-2-2-2-2000000000000-20000002-2-2222-20000000022-2-2-2-2220000000000
χ2622222-222-22222222-22-22-20000-2-2-2-2000000000000-2000000-222-222-200000000-2-22222-2-20000000000
χ2722222-2-2-2-2222-2-2-2-22-222-22i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i000020000−2i2i0000-22-20000−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-22-222-2−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i0000200002i−2i0000-22-200002i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ302222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1111122-2-2-2-2-1-1-11111-1-1-1-1111111110000000000
χ312222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-11111111111110000000000
χ322222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-111111111-2-2-2-2-11111-2-22222-1-1-111111111-1-1-1-1-1-1-1-10000000000
χ332222-12222-1-1-1-1-1-1-1-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001−i3i3−i3i3-2-20000111−i3i3−i3i31111−i3i3−i3i3−i3i3−i3i30000000000
χ342222-12222-1-1-1-1-1-1-1-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001i3−i3i3−i3-2-20000111i3−i3i3−i31111i3−i3i3−i3i3−i3i3−i30000000000
χ352222-12222-1-1-1-1-1-1-1-2-22-2-2-2-2-2-2-1-1-1-11111111100001−i3i3−i3i3220000111−i3i3−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i30000000000
χ362222-12222-1-1-1-1-1-1-1-2-22-2-2-2-2-2-2-1-1-1-11111111100001i3−i3i3−i3220000111i3−i3i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i30000000000
χ372222-12-2-22-1-1-1111122-2-2-2000011-1-133−3−333−3−30000-1−i3i3−i3i3002i−2i2i−2i-111i3−i3i3−i33−33−3−i−iii−i−iii0000000000
χ382222-12-2-22-1-1-1111122-2-2-2000011-1-133−3−333−3−30000-1i3−i3i3−i300−2i2i−2i2i-111−i3i3−i3i33−33−3ii−i−iii−i−i0000000000
χ392222-12-2-22-1-1-1111122-2-2-2000011-1-1−3−333−3−3330000-1−i3i3−i3i300−2i2i−2i2i-111i3−i3i3−i3−33−33ii−i−iii−i−i0000000000
χ402222-12-2-22-1-1-1111122-2-2-2000011-1-1−3−333−3−3330000-1i3−i3i3−i3002i−2i2i−2i-111−i3i3−i3i3−33−33−i−iii−i−iii0000000000
χ412222-12-2-22-1-1-11111-2-2-222000011-1-133−3−333−3−322-2-21-1-1-1-10000001-1-11111−33−333−3−333−3−330000000000
χ422222-12-2-22-1-1-11111-2-2-222000011-1-133−3−333−3−3-2-222111110000001-1-1-1-1-1-1−33−33−333−3−333−30000000000
χ432222-12-2-22-1-1-11111-2-2-222000011-1-1−3−333−3−33322-2-21-1-1-1-10000001-1-111113−33−3−333−3−333−30000000000
χ442222-12-2-22-1-1-11111-2-2-222000011-1-1−3−333−3−333-2-222111110000001-1-1-1-1-1-13−33−33−3−333−3−330000000000
χ452222-1-222-2-1-1-1-1-1-1-12-2-2-2200001111−i3−i3i3i3i3i3−i3−i32-2-22-1-1-11100000011-111-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000
χ462222-1-222-2-1-1-1-1-1-1-12-2-2-2200001111−i3−i3i3i3i3i3−i3−i3-222-2-111-1-100000011-1-1-111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000
χ472222-1-222-2-1-1-1-1-1-1-12-2-2-2200001111i3i3−i3−i3−i3−i3i3i32-2-22-1-1-11100000011-111-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000
χ482222-1-222-2-1-1-1-1-1-1-12-2-2-2200001111i3i3−i3−i3−i3−i3i3i3-222-2-111-1-100000011-1-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000
χ492222-1-222-2-1-1-1-1-1-1-1-22-22-200001111−i3−i3i3i3i3i3−i3−i300001−i3i3i3−i3002-2-22-1-11i3−i3−i3i3−i3i3i3−i3-1-11111-1-10000000000
χ502222-1-222-2-1-1-1-1-1-1-1-22-22-200001111−i3−i3i3i3i3i3−i3−i300001i3−i3−i3i300-222-2-1-11−i3i3i3−i3−i3i3i3−i311-1-1-1-1110000000000
χ512222-1-222-2-1-1-1-1-1-1-1-22-22-200001111i3i3−i3−i3−i3−i3i3i300001−i3i3i3−i300-222-2-1-11i3−i3−i3i3i3−i3−i3i311-1-1-1-1110000000000
χ522222-1-222-2-1-1-1-1-1-1-1-22-22-200001111i3i3−i3−i3−i3−i3i3i300001i3−i3−i3i3002-2-22-1-11−i3i3i3−i3i3−i3−i3i3-1-11111-1-10000000000
χ532222-1-2-2-2-2-1-1-111112-222-22i2i−2i−2i-1-111−i−i−i−iiiii0000-1−i3i3i3−i3−2i2i00001-11−i3i3i3−i3ii−i−i3−33−3−33−330000000000
χ542222-1-2-2-2-2-1-1-111112-222-22i2i−2i−2i-1-111−i−i−i−iiiii0000-1i3−i3−i3i3−2i2i00001-11i3−i3−i3i3ii−i−i−33−333−33−30000000000
χ552222-1-2-2-2-2-1-1-111112-222-2−2i−2i2i2i-1-111iiii−i−i−i−i0000-1−i3i3i3−i32i−2i00001-11−i3i3i3−i3−i−iii−33−333−33−30000000000
χ562222-1-2-2-2-2-1-1-111112-222-2−2i−2i2i2i-1-111iiii−i−i−i−i0000-1i3−i3−i3i32i−2i00001-11i3−i3−i3i3−i−iii3−33−3−33−330000000000
χ572222-1-2-2-2-2-1-1-11111-222-222i2i−2i−2i-1-111−i−i−i−iiiii2-22-21-1-1112i−2i2i2i−2i−2i-11-1-1-111−i−iii−i−i−i−iiiii0000000000
χ582222-1-2-2-2-2-1-1-11111-222-222i2i−2i−2i-1-111−i−i−i−iiiii-22-22111-1-12i−2i−2i−2i2i2i-11-111-1-1−i−iiiiiii−i−i−i−i0000000000
χ592222-1-2-2-2-2-1-1-11111-222-22−2i−2i2i2i-1-111iiii−i−i−i−i2-22-21-1-111−2i2i−2i−2i2i2i-11-1-1-111ii−i−iiiii−i−i−i−i0000000000
χ602222-1-2-2-2-2-1-1-11111-222-22−2i−2i2i2i-1-111iiii−i−i−i−i-22-22111-1-1−2i2i2i2i−2i−2i-11-111-1-1ii−i−i−i−i−i−iiiii0000000000
χ6144-4-44400-44-4-400000000022−2222−22004-422−2222−2222−2222−2200000000000000000000000000000000000000000000
χ6244-4-44400-44-4-4000000000−2222−2222004-4−2222−2222−2222−222200000000000000000000000000000000000000000000
χ6344-4-44-40044-4-4000000000−2i22i22i2−2i200-44−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ6444-4-44-40044-4-40000000002i2−2i2−2i22i200-442i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ6544-4-4-2400-4-2222323−23−230000022−2222−2223−23-222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000000000
χ6644-4-4-2400-4-2222323−23−2300000−2222−222223−23-22−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000000000
χ6744-4-4-2400-4-222−23−2323230000022−2222−22−2323-222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000
χ6844-4-4-2400-4-222−23−23232300000−2222−2222−2323-22−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000
χ6944-4-4-2-4004-2222323−23−2300000−2i22i22i2−2i2−23232-22ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000000000
χ7044-4-4-2-4004-2222323−23−23000002i2−2i2−2i22i2−23232-2−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000000000
χ7144-4-4-2-4004-222−23−23232300000−2i22i22i2−2i223−232-22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000000000
χ7244-4-4-2-4004-222−23−232323000002i2−2i2−2i22i223−232-2−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000
χ734-44-4404i−4i0-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ744-44-4404i−4i0-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ754-44-440−4i4i0-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ764-44-440−4i4i0-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ778-88-8-408i−8i04-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ788-88-8-40−8i8i04-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000
χ798-8-8880000-8-88000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-4000044-4−4i34i34i3−4i300000000000000000000000000000000000000000000000000000000000000000
χ818-8-88-4000044-44i3−4i3−4i34i300000000000000000000000000000000000000000000000000000000000000000

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