Finite Group Databasebeta

← Group #10692425

Character table — Group #10692425

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888888888888888888888888888824242424484848484848
order122234444666121212122444488881212121224242424242424244444688888812121212121212121212122424242424242424242424248888248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ8111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ911111-1-1-1-1111-1-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i1-11-1-1i−iii−i−i11-11111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i1-1i−i1-1
χ1011111-1-1-1-1111-1-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i1-11-1-1i−iii−i−i11-11111-1-1-1-1ii−i−iiiii−i−i−i−i−i−iii-11−ii-11
χ1111111-1-1-1-1111-1-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i-11-11-1i−i−i−iii11-1-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i1-1−ii-11
χ1211111-1-1-1-1111-1-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i-11-11-1i−i−i−iii11-1-1-1-1-11111ii−i−i−i−i−i−iiiii−i−iii-11i−i1-1
χ1311111-1-1-1-1111-1-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii1-11-1-1−ii−i−iii11-11111-1-1-1-1−i−iii−i−i−i−iiiiiii−i−i-11i−i-11
χ1411111-1-1-1-1111-1-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii1-11-1-1−ii−i−iii11-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii1-1−ii1-1
χ1511111-1-1-1-1111-1-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii-11-11-1−iiii−i−i11-1-1-1-1-11111−i−iiiiiii−i−i−i−iii−i−i-11−ii1-1
χ1611111-1-1-1-1111-1-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii-11-11-1−iiii−i−i11-1-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii1-1i−i-11
χ172222222222222222-22-2-2-222222222222222220000-2-2-20000-2-2-200000000-2-2-2-2000000000000000000
χ182222222222222222-22-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000-2220000-2-2-2000000002222000000000000000000
χ19222222-2-22222-2-2-2-22-22-2-20000-2-2220000000000002002i−2i2i−2i-22-20000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ20222222-2-22222-2-2-2-22-22-2-20000-2-222000000000000200−2i2i−2i2i-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ21222222-2-22222-2-2-2-2-2-2-2220000-2-2220000000022-2-2-20000002-2222-2-222-2-20000000000000000000000
χ22222222-2-22222-2-2-2-2-2-2-2220000-2-22200000000-2-222-20000002-22-2-222-2-2220000000000000000000000
χ2322222-222-222222222-2-22-20000-2-2-2-2000000002-2-2220000002-2-222-2-2-2-2220000000000000000000000
χ2422222-222-222222222-2-22-20000-2-2-2-200000000-222-220000002-2-2-2-22222-2-20000000000000000000000
χ2522222-222-22222222-2-22-220000-2-2-2-2000000000000-2002-2-22-22200000000000022-2-2-2-2220000000000
χ2622222-222-22222222-2-22-220000-2-2-2-2000000000000-200-222-2-222000000000000-2-22222-2-20000000000
χ2722222-2-2-2-2222-2-2-2-222-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i00002−2i2i0000-2-2200000000−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-222-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i000022i−2i0000-2-22000000002i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ302222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-122-2-2-2-2-1-1-111111111-1-1-1-1111111110000000000
χ312222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1111111112222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111111110000000000
χ322222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-111111111-2-2-2-2-1-2-22222-1-1-1111111111111-1-1-1-1-1-1-1-10000000000
χ332222-12222-1-1-1-1-1-1-1-22-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001-2-20000111−i3i3−i3i3−i3i3−i3i31111−i3i3−i3i3−i3i3−i3i30000000000
χ342222-12222-1-1-1-1-1-1-1-22-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100001-2-20000111i3−i3i3−i3i3−i3i3−i31111i3−i3i3−i3i3−i3i3−i30000000000
χ352222-12222-1-1-1-1-1-1-1-22-2-2-2-2-2-2-2-1-1-1-11111111100001220000111−i3i3−i3i3−i3i3−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i30000000000
χ362222-12222-1-1-1-1-1-1-1-22-2-2-2-2-2-2-2-1-1-1-11111111100001220000111i3−i3i3−i3i3−i3i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i30000000000
χ372222-12-2-22-1-1-111112-22-2-2000011-1-133−3−333−3−30000-1002i−2i2i−2i1-11−i3i3i3−i3−i3i3i3−i33−33−3−i−iii−i−iii0000000000
χ382222-12-2-22-1-1-111112-22-2-2000011-1-133−3−333−3−30000-100−2i2i−2i2i1-11i3−i3−i3i3i3−i3−i3i33−33−3ii−i−iii−i−i0000000000
χ392222-12-2-22-1-1-111112-22-2-2000011-1-1−3−333−3−3330000-1002i−2i2i−2i1-11i3−i3−i3i3i3−i3−i3i3−33−33−i−iii−i−iii0000000000
χ402222-12-2-22-1-1-111112-22-2-2000011-1-1−3−333−3−3330000-100−2i2i−2i2i1-11−i3i3i3−i3−i3i3i3−i3−33−33ii−i−iii−i−i0000000000
χ412222-12-2-22-1-1-11111-2-2-222000011-1-133−3−333−3−322-2-21000000-11-1-1-111-1-111−33−333−3−333−3−330000000000
χ422222-12-2-22-1-1-11111-2-2-222000011-1-133−3−333−3−3-2-2221000000-11-111-1-111-1-1−33−33−333−3−333−30000000000
χ432222-12-2-22-1-1-11111-2-2-222000011-1-1−3−333−3−33322-2-21000000-11-1-1-111-1-1113−33−3−333−3−333−30000000000
χ442222-12-2-22-1-1-11111-2-2-222000011-1-1−3−333−3−333-2-2221000000-11-111-1-111-1-13−33−33−3−333−3−330000000000
χ452222-1-222-2-1-1-1-1-1-1-12-2-22-200001111−i3−i3i3i3i3i3−i3−i32-2-22-1000000-111-1-11111-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000
χ462222-1-222-2-1-1-1-1-1-1-12-2-22-200001111−i3−i3i3i3i3i3−i3−i3-222-2-1000000-11111-1-1-1-111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000000000
χ472222-1-222-2-1-1-1-1-1-1-12-2-22-200001111i3i3−i3−i3−i3−i3i3i32-2-22-1000000-111-1-11111-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000
χ482222-1-222-2-1-1-1-1-1-1-12-2-22-200001111i3i3−i3−i3−i3−i3i3i3-222-2-1000000-11111-1-1-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000000000
χ492222-1-222-2-1-1-1-1-1-1-1-2-22-2200001111−i3−i3i3i3i3i3−i3−i300001002-2-221-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-1-11111-1-10000000000
χ502222-1-222-2-1-1-1-1-1-1-1-2-22-2200001111−i3−i3i3i3i3i3−i3−i30000100-222-21-1-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i311-1-1-1-1110000000000
χ512222-1-222-2-1-1-1-1-1-1-1-2-22-2200001111i3i3−i3−i3−i3−i3i3i300001002-2-221-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-1-11111-1-10000000000
χ522222-1-222-2-1-1-1-1-1-1-1-2-22-2200001111i3i3−i3−i3−i3−i3i3i30000100-222-21-1-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i311-1-1-1-1110000000000
χ532222-1-2-2-2-2-1-1-1111122-2-222i2i−2i−2i-1-111−i−i−i−iiiii0000-1−2i2i000011-1−i3i3−i3i3i3−i3i3−i3ii−i−i3−33−3−33−330000000000
χ542222-1-2-2-2-2-1-1-1111122-2-222i2i−2i−2i-1-111−i−i−i−iiiii0000-1−2i2i000011-1i3−i3i3−i3−i3i3−i3i3ii−i−i−33−333−33−30000000000
χ552222-1-2-2-2-2-1-1-1111122-2-22−2i−2i2i2i-1-111iiii−i−i−i−i0000-12i−2i000011-1−i3i3−i3i3i3−i3i3−i3−i−iii−33−333−33−30000000000
χ562222-1-2-2-2-2-1-1-1111122-2-22−2i−2i2i2i-1-111iiii−i−i−i−i0000-12i−2i000011-1i3−i3i3−i3−i3i3−i3i3−i−iii3−33−3−33−330000000000
χ572222-1-2-2-2-2-1-1-11111-2222-22i2i−2i−2i-1-111−i−i−i−iiiii2-22-212i−2i2i2i−2i−2i-1-11-1-1-1-11111−i−iii−i−i−i−iiiii0000000000
χ582222-1-2-2-2-2-1-1-11111-2222-22i2i−2i−2i-1-111−i−i−i−iiiii-22-2212i−2i−2i−2i2i2i-1-111111-1-1-1-1−i−iiiiiii−i−i−i−i0000000000
χ592222-1-2-2-2-2-1-1-11111-2222-2−2i−2i2i2i-1-111iiii−i−i−i−i2-22-21−2i2i−2i−2i2i2i-1-11-1-1-1-11111ii−i−iiiii−i−i−i−i0000000000
χ602222-1-2-2-2-2-1-1-11111-2222-2−2i−2i2i2i-1-111iiii−i−i−i−i-22-221−2i2i2i2i−2i−2i-1-111111-1-1-1-1ii−i−i−i−i−i−iiiii0000000000
χ614-44-4404i−4i0-44-44i4i−4i−4i00000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ624-44-4404i−4i0-44-44i4i−4i−4i0000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ634-44-440−4i4i0-44-4−4i−4i4i4i0000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ644-44-440−4i4i0-44-4−4i−4i4i4i00000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ654-4-444400-4-4-44000000000−2i22i2−2i22i2004-4−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ664-4-444400-4-4-440000000002i2−2i22i2−2i2004-42i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ674-4-444-4004-4-4400000000022−22−222200-4422−2222−22−2222−222200000000000000000000000000000000000000000000
χ684-4-444-4004-4-44000000000−222222−2200-44−2222−222222−2222−2200000000000000000000000000000000000000000000
χ694-4-44-2400-422-223−2323−2300000−2i22i2−2i22i223−23-222ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000000000
χ704-4-44-2400-422-223−2323−23000002i2−2i22i2−2i223−23-22−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000000000
χ714-4-44-2400-422-2−2323−232300000−2i22i2−2i22i2−2323-222ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000
χ724-4-44-2400-422-2−2323−2323000002i2−2i22i2−2i2−2323-22−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000000000
χ734-4-44-2-400422-223−2323−230000022−22−2222−23232-22ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000000000
χ744-4-44-2-400422-223−2323−2300000−222222−22−23232-2−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000000000
χ754-4-44-2-400422-2−2323−23230000022−22−222223−232-22ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000
χ764-4-44-2-400422-2−2323−232300000−222222−2223−232-2−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000
χ7788-8-8800008-8-8000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-40000-444−4i34i34i3−4i300000000000000000000000000000000000000000000000000000000000000000
χ7988-8-8-40000-4444i3−4i3−4i34i300000000000000000000000000000000000000000000000000000000000000000
χ808-88-8-408i−8i04-44−4i−4i4i4i00000000000000000000000000000000000000000000000000000000000000000
χ818-88-8-40−8i8i04-444i4i−4i−4i00000000000000000000000000000000000000000000000000000000000000000

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