Finite Group Databasebeta

← Group #10712676

Character table — Group #10712676

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888888888888888888888888888824242424484848484848
order122222223666666622222444466661212121212121212226666666688888888242424242424242424242424242424242244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ61111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ71111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ81111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ91111-1-111111-1-1-1-1111-1111-1-1111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11-1
χ101111-1-111111-1-1-1-1111-1111-1-1111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-11
χ111111-1-111111-1-1-1-1111-1111-1-1111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-11-1-11-11
χ121111-1-111111-1-1-1-1111-1111-1-1111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-111-11-1
χ131111-1-111111-1-1-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ141111-1-111111-1-1-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1111-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ151111-1-111111-1-1-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ161111-1-111111-1-1-1-1111-1-1-1-111-111-1-1-1-11111-1-1-1111-1-1-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ172222222222222222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-2-2-222220000000000000000000000000000000000
χ182222222222222222-2-22-2-22222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ1922222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ2022222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000
χ2122222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1111111112-2-1-1-1-111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii0000000000
χ2222222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-1-1-1111111112-2-1-1-1-11111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i0000000000
χ2322222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-111111111-221111-1-1-1-10000000033−3−333−3−333−3−333−3−30000000000
χ2422222222-1-1-1-1-1-1-1-1-2-2222-2-2-2-2-1-1-1-111111111-221111-1-1-1-100000000−3−333−3−333−3−333−3−3330000000000
χ2522222222-1-1-1-1-1-1-1-1-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000
χ2622222222-1-1-1-1-1-1-1-1-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000
χ272222-2-222222-2-2-2-22-2-2-222-222-222-2-2-2-22222-2-22-2-2-22222-2-20000000000000000000000000000000000
χ282222-2-222222-2-2-2-22-2-2-2-2-22-2-2222-2-222-2-2-2-22222-2-222-2-2220000000000000000000000000000000000
χ292222-2-222-1-1-11111-122-2222-2-22-1-111-1-11111-1-1-2-2-1-111-1-11122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000
χ302222-2-222-1-1-11111-122-2222-2-22-1-111-1-11111-1-1-2-2-1-111-1-111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000
χ312222-2-222-1-1-11111-122-2-2-2-222-2-1-11111-1-1-1-111-22-1-11111-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000
χ322222-2-222-1-1-11111-122-2-2-2-222-2-1-11111-1-1-1-111-22-1-11111-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000
χ332222-2-222-1-1-11111-1-2-2-222-222-2-1-11111-1-1-1-1112-211-1-1-1-1110000000033−3−3−3−33333−3−3−3−3330000000000
χ342222-2-222-1-1-11111-1-2-2-222-222-2-1-11111-1-1-1-1112-211-1-1-1-11100000000−3−33333−3−3−3−33333−3−30000000000
χ352222-2-222-1-1-11111-1-2-2-2-2-22-2-22-1-111-1-11111-1-12211-1-111-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000
χ362222-2-222-1-1-11111-1-2-2-2-2-22-2-22-1-111-1-11111-1-12211-1-111-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000
χ372-22-2002-22-2-2000022-202-2200-22-200220000-2-2002-2002-200002i−2i002i−2i00002i−2i2i−2i00002i−2i2i−2i0000000000
χ382-22-2002-22-2-2000022-202-2200-22-200220000-2-2002-2002-20000−2i2i00−2i2i0000−2i2i−2i2i0000−2i2i−2i2i0000000000
χ392-22-2002-22-2-2000022-20-22-20022-200-2-2000022002-200-2200002-200-2200002-22-20000-22-220000000000
χ402-22-2002-22-2-2000022-20-22-20022-200-2-2000022002-200-220000-22002-20000-22-2200002-22-20000000000
χ412-22-2002-22-2-200002-2202-2-20022-200-2-200002200-22002-2002-2002-2002-22-200002-22-200000000000000
χ422-22-2002-22-2-200002-2202-2-20022-200-2-200002200-22002-200-2200-2200-22-220000-22-2200000000000000
χ432-22-2002-22-2-200002-220-22200-22-200220000-2-200-2200-22002i−2i00−2i2i002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ442-22-2002-22-2-200002-220-22200-22-200220000-2-200-2200-2200−2i2i002i−2i00−2i2i−2i2i00002i−2i2i−2i00000000000000
χ452-22-2002-2-111−i3−i3i3i3-12-202-2200-2-11−i3i3-1-1−i3−i3i3i31100-11−i3i3-11−i3i3002i−2i002i−2i3−3−33−ii−ii3−3−33−ii−ii0000000000
χ462-22-2002-2-111−i3−i3i3i3-12-202-2200-2-11−i3i3-1-1−i3−i3i3i31100-11−i3i3-11−i3i300−2i2i00−2i2i−333−3i−ii−i−333−3i−ii−i0000000000
χ472-22-2002-2-111−i3−i3i3i3-12-20-22-2002-11−i3i311i3i3−i3−i3-1-100-11−i3i31-1i3−i3002-200-22−i3i3i3−i3-11-11i3−i3−i3i31-11-10000000000
χ482-22-2002-2-111−i3−i3i3i3-12-20-22-2002-11−i3i311i3i3−i3−i3-1-100-11−i3i31-1i3−i300-22002-2i3−i3−i3i31-11-1−i3i3i3−i3-11-110000000000
χ492-22-2002-2-111−i3−i3i3i3-1-2202-2-2002-11−i3i311i3i3−i3−i3-1-1001-1i3−i3-11−i3i32-2002-200-11-11−i3i3i3−i3-11-11−i3i3i3−i30000000000
χ502-22-2002-2-111−i3−i3i3i3-1-2202-2-2002-11−i3i311i3i3−i3−i3-1-1001-1i3−i3-11−i3i3-2200-22001-11-1i3−i3−i3i31-11-1i3−i3−i3i30000000000
χ512-22-2002-2-111−i3−i3i3i3-1-220-22200-2-11−i3i3-1-1−i3−i3i3i311001-1i3−i31-1i3−i32i−2i00−2i2i00−ii−ii3−3−33i−ii−i−333−30000000000
χ522-22-2002-2-111−i3−i3i3i3-1-220-22200-2-11−i3i3-1-1−i3−i3i3i311001-1i3−i31-1i3−i3−2i2i002i−2i00i−ii−i−333−3−ii−ii3−3−330000000000
χ532-22-2002-2-111i3i3−i3−i3-12-202-2200-2-11i3−i3-1-1i3i3−i3−i31100-11i3−i3-11i3−i3002i−2i002i−2i−333−3−ii−ii−333−3−ii−ii0000000000
χ542-22-2002-2-111i3i3−i3−i3-12-202-2200-2-11i3−i3-1-1i3i3−i3−i31100-11i3−i3-11i3−i300−2i2i00−2i2i3−3−33i−ii−i3−3−33i−ii−i0000000000
χ552-22-2002-2-111i3i3−i3−i3-12-20-22-2002-11i3−i311−i3−i3i3i3-1-100-11i3−i31-1−i3i3002-200-22i3−i3−i3i3-11-11−i3i3i3−i31-11-10000000000
χ562-22-2002-2-111i3i3−i3−i3-12-20-22-2002-11i3−i311−i3−i3i3i3-1-100-11i3−i31-1−i3i300-22002-2−i3i3i3−i31-11-1i3−i3−i3i3-11-110000000000
χ572-22-2002-2-111i3i3−i3−i3-1-2202-2-2002-11i3−i311−i3−i3i3i3-1-1001-1−i3i3-11i3−i32-2002-200-11-11i3−i3−i3i3-11-11i3−i3−i3i30000000000
χ582-22-2002-2-111i3i3−i3−i3-1-2202-2-2002-11i3−i311−i3−i3i3i3-1-1001-1−i3i3-11i3−i3-2200-22001-11-1−i3i3i3−i31-11-1−i3i3i3−i30000000000
χ592-22-2002-2-111i3i3−i3−i3-1-220-22200-2-11i3−i3-1-1i3i3−i3−i311001-1−i3i31-1−i3i32i−2i00−2i2i00−ii−ii−333−3i−ii−i3−3−330000000000
χ602-22-2002-2-111i3i3−i3−i3-1-220-22200-2-11i3−i3-1-1i3i3−i3−i311001-1−i3i31-1−i3i3−2i2i002i−2i00i−ii−i3−3−33−ii−ii−333−30000000000
χ61444444-4-44444444400-4000000-4-4-4-40000000000000000000000000000000000000000000000000000
χ62444444-4-4-2-2-2-2-2-2-2-200-40000002222−2i32i3−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ63444444-4-4-2-2-2-2-2-2-2-200-400000022222i3−2i32i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ644444-4-4-4-4444-4-4-4-44004000000-4-4440000000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-2-2-22222-200400000022-2-2−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ664444-4-4-4-4-2-2-22222-200400000022-2-22i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ674-44-400-444-4-4000040000004-40-4400004-4-440000000000000000000000000000000000000000000000
χ684-44-400-444-4-400004000000-440-440000-444-40000000000000000000000000000000000000000000000
χ694-44-400-44-222−2i3−2i32i32i3-20000004-402-22i3−2i3−2i32i3-222-22i3−2i300000000000000000000000000000000000000000000
χ704-44-400-44-222−2i3−2i32i32i3-2000000-4402-22i3−2i32i3−2i32-2-22−2i32i300000000000000000000000000000000000000000000
χ714-44-400-44-2222i32i3−2i3−2i3-20000004-402-2−2i32i32i3−2i3-222-2−2i32i300000000000000000000000000000000000000000000
χ724-44-400-44-2222i32i3−2i3−2i3-2000000-4402-2−2i32i3−2i32i32-2-222i3−2i300000000000000000000000000000000000000000000
χ734-4-444-40044-44-44-4-400000000000000000000000000000000000000000000000000000002-22-2000000
χ744-4-444-40044-44-44-4-40000000000000000000000000000000000000000000000000000000-22-22000000
χ754-4-44-440044-4-44-44-400000000000000000000000000000000000000000000000000000002-2-22000000
χ764-4-44-440044-4-44-44-40000000000000000000000000000000000000000000000000000000-222-2000000
χ7788-8-800008-880000-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-80000-44-4−4i34i34i3−4i3400000000000000000000000000000000000000000000000000000000000000000
χ7988-8-80000-44-44i3−4i3−4i34i3400000000000000000000000000000000000000000000000000000000000000000
χ808-8-888-800-4-44-44-44400000000000000000000000000000000000000000000000000000000000000000
χ818-8-88-8800-4-444-44-4400000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).