Finite Group Databasebeta

← Group #13167586

Character table — Group #13167586

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444448888888888888888888899991818181818181818181818181818181818181818181818181818181818181818181836363636363636367272727272727272
order1222223666666633666666336666666666666666662222224444444466666666121212121212121212121212121212122244444466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111-1-11111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111-1-11111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111-1-11111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111-1-11111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ911-1-11-111-1-111-1-1111-1-1-1-11111-11-111-1-1-1-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-11-1i−ii−i
χ1011-1-11-111-1-111-1-1111-1-1-1-11111-11-111-1-1-1-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11-11−ii−ii
χ1111-1-11-111-1-111-1-1111-1-1-1-11111-11-111-1-1-1-11111-1-1-1-111-1-11-1−i−iii−i−iii11-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-11-1−ii−ii
χ1211-1-11-111-1-111-1-1111-1-1-1-11111-11-111-1-1-1-11111-1-1-1-111-1-11-1−i−iii−i−iii11-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11-11i−ii−i
χ1311-1-1-1111-1-1-1-111111-1-1-1-1111-11-1111-1-1-1-1-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-1-111-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ1411-1-1-1111-1-1-1-111111-1-1-1-1111-11-1111-1-1-1-1-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-1-111-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ1511-1-1-1111-1-1-1-111111-1-1-1-1111-11-1111-1-1-1-1-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ1611-1-1-1111-1-1-1-111111-1-1-1-1111-11-1111-1-1-1-1-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
χ17222222222222222222222222222222222222222222-2-2-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ19222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ20222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111111133−3−333−3−333−3−333−3−30000000000000000
χ21222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-20000000011111111−3−333−3−333−3−333−3−3330000000000000000
χ222222-2-22222-2-2-2-22222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2-22222-200000000000000000000000000000000
χ232222-2-2-1-1-1-1111122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112222-2-22222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000000000000000
χ242222-2-2-1-1-1-1111122222222-1-1-2-2-2-2-1-1-1-1-1-1111111112222-2-2-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-10000000000000000
χ252222-2-2-1-1-1-1111122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111-1-1-1-1133−3−333−3−3−3−333−3−3330000000000000000
χ262222-2-2-1-1-1-1111122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111-1-1-1-11−3−333−3−33333−3−333−3−30000000000000000
χ2722-2-22-222-2-222-2-2222-2-2-2-22222-22-222-2-2-2-22222-2-2-2-2-2-222-2200000000-2-22-2-222200000000000000000000000000000000
χ2822-2-22-2-1-111-1-111222-2-2-2-22-1-12-22-2-1-11111-1-1-1-1111122-2-22-22i2i−2i−2i2i2i−2i−2i-1-11-1-1111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ2922-2-22-2-1-111-1-111222-2-2-2-22-1-12-22-2-1-11111-1-1-1-1111122-2-22-2−2i−2i2i2i−2i−2i2i2i-1-11-1-1111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ3022-2-22-2-1-111-1-111222-2-2-2-22-1-12-22-2-1-11111-1-1-1-11111-2-222-220000000011-111-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3122-2-22-2-1-111-1-111222-2-2-2-22-1-12-22-2-1-11111-1-1-1-11111-2-222-220000000011-111-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3222-2-2-2222-2-2-2-222222-2-2-2-2222-22-2222-2-2-2-2-2-2-2-22222-2-2222-200000000-2-2222-2-2200000000000000000000000000000000
χ3322-2-2-22-1-11111-1-1222-2-2-2-22-1-1-22-22-1-111111111-1-1-1-122-2-2-222i2i−2i−2i−2i−2i2i2i-1-1111-1-11−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ3422-2-2-22-1-11111-1-1222-2-2-2-22-1-1-22-22-1-111111111-1-1-1-122-2-2-22−2i−2i2i2i2i2i−2i−2i-1-1111-1-11iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ3522-2-2-22-1-11111-1-1222-2-2-2-22-1-1-22-22-1-111111111-1-1-1-1-2-2222-20000000011-1-1-111-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622-2-2-22-1-11111-1-1222-2-2-2-22-1-1-22-22-1-111111111-1-1-1-1-2-2222-20000000011-1-1-111-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372-22-2002-22-2000022-22-22-2-2220000-2-222-2-2000000002-22-20000002i−2i2i−2i2-220000-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-22-2002-22-2000022-22-22-2-2220000-2-222-2-2000000002-22-2000000−2i2i−2i2i2-220000-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-22-2002-22-2000022-22-22-2-2220000-2-222-2-200000000-22-22002-22-20000-22-2000022-22-22-22-2000000000000000000000000
χ402-22-2002-22-2000022-22-22-2-2220000-2-222-2-200000000-22-2200-22-220000-22-200002-22-22-22-22000000000000000000000000
χ412-22-200-11-11−i3i3−i3i322-22-22-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i32-22-20000002i−2i2i−2i-11-1−i3i3−i3i313−3−333−3−33−ii−ii−ii−ii0000000000000000
χ422-22-200-11-11−i3i3−i3i322-22-22-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i32-22-2000000−2i2i−2i2i-11-1−i3i3−i3i31−333−3−333−3i−ii−ii−ii−i0000000000000000
χ432-22-200-11-11−i3i3−i3i322-22-22-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-22-22002-22-200001-11i3−i3i3−i3-1-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ442-22-200-11-11−i3i3−i3i322-22-22-2-2-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-22-2200-22-2200001-11i3−i3i3−i3-11-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ452-22-200-11-11i3−i3i3−i322-22-22-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i32-22-20000002i−2i2i−2i-11-1i3−i3i3−i31−333−3−333−3−ii−ii−ii−ii0000000000000000
χ462-22-200-11-11i3−i3i3−i322-22-22-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i32-22-2000000−2i2i−2i2i-11-1i3−i3i3−i313−3−333−3−33i−ii−ii−ii−i0000000000000000
χ472-22-200-11-11i3−i3i3−i322-22-22-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-22-22002-22-200001-11−i3i3−i3i3-1-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ482-22-200-11-11i3−i3i3−i322-22-22-2-2-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-22-2200-22-2200001-11−i3i3−i3i3-11-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ492-2-22002-2-22000022-2-22-22-2220000-2-2-2-222000000002-2-220000002-2-222-2-200002000000002-22-2-22-220000000000000000
χ502-2-22002-2-22000022-2-22-22-2220000-2-2-2-222000000002-2-22000000-222-22-2-20000200000000-22-222-22-20000000000000000
χ512-2-22002-2-22000022-2-22-22-2220000-2-2-2-22200000000-222-2002i−2i−2i2i0000-2220000-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ522-2-22002-2-22000022-2-22-22-2220000-2-2-2-22200000000-222-200−2i2i2i−2i0000-2220000-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ532-2-2200-111-1−i3i3i3−i322-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i32-2-220000002-2-22-111−i3i3i3−i3-1−i3i3i3−i3i3−i3−i3i3-11-111-11-10000000000000000
χ542-2-2200-111-1−i3i3i3−i322-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i32-2-22000000-222-2-111−i3i3i3−i3-1i3−i3−i3i3−i3i3i3−i31-11-1-11-110000000000000000
χ552-2-2200-111-1−i3i3i3−i322-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-222-2002i−2i−2i2i00001-1-1i3−i3−i3i31−ii−iii−ii−i3−3−33−333−30000000000000000
χ562-2-2200-111-1−i3i3i3−i322-2-22-22-2-1-100001111-1-1−i3−i3i3i3i3i3−i3−i3-222-200−2i2i2i−2i00001-1-1i3−i3−i3i31i−ii−i−ii−ii−333−33−3−330000000000000000
χ572-2-2200-111-1i3−i3−i3i322-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i32-2-220000002-2-22-111i3−i3−i3i3-1i3−i3−i3i3−i3i3i3−i3-11-111-11-10000000000000000
χ582-2-2200-111-1i3−i3−i3i322-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i32-2-22000000-222-2-111i3−i3−i3i3-1−i3i3i3−i3i3−i3−i3i31-11-1-11-110000000000000000
χ592-2-2200-111-1i3−i3−i3i322-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-222-2002i−2i−2i2i00001-1-1−i3i3i3−i31−ii−iii−ii−i−333−33−3−330000000000000000
χ602-2-2200-111-1i3−i3−i3i322-2-22-22-2-1-100001111-1-1i3i3−i3−i3−i3−i3i3i3-222-200−2i2i2i−2i00001-1-1−i3i3i3−i31i−ii−i−ii−ii3−3−33−333−30000000000000000
χ61444444444444441-21-2-211-21-211-2-21-21-21-21-21-21-21-200000000000000000000000000000000000000000022220000-1-1-1-1
χ62444444444444441-21-2-211-21-211-2-21-21-21-21-21-21-21-2000000000000000000000000000000000000000000-2-2-2-200001111
χ6344444444444444-21-211-2-21-21-2-211-21-21-21-21-21-21-210000000000000000000000000000000000000022220000-1-1-1-10000
χ6444444444444444-21-211-2-21-21-2-211-21-21-21-21-21-21-2100000000000000000000000000000000000000-2-2-2-2000011110000
χ654444-4-44444-4-4-4-41-21-2-211-21-2-1-1221-21-21-2-12-12-12-1200000000000000000000000000000000000000000022-2-20000-1-111
χ664444-4-44444-4-4-4-41-21-2-211-21-2-1-1221-21-21-2-12-12-12-12000000000000000000000000000000000000000000-2-222000011-1-1
χ674444-4-44444-4-4-4-4-21-211-2-21-2122-1-1-21-21-212-12-12-12-10000000000000000000000000000000000000022-2-20000-1-1110000
χ684444-4-44444-4-4-4-4-21-211-2-21-2122-1-1-21-21-212-12-12-12-100000000000000000000000000000000000000-2-222000011-1-10000
χ6944-4-44-444-4-444-4-41-2122-1-1-21-21-1-221-2-12-121-21-2-12-120000000000000000000000000000000000000000002i−2i2i−2i0000−ii−ii
χ7044-4-44-444-4-444-4-41-2122-1-1-21-21-1-221-2-12-121-21-2-12-12000000000000000000000000000000000000000000−2i2i−2i2i0000i−ii−i
χ7144-4-44-444-4-444-4-4-21-2-1-1221-21-221-1-212-12-1-21-212-12-1000000000000000000000000000000000000002-22-20000-11-110000
χ7244-4-44-444-4-444-4-4-21-2-1-1221-21-221-1-212-12-1-21-212-12-100000000000000000000000000000000000000-22-2200001-11-10000
χ7344-4-4-4444-4-4-4-4441-2122-1-1-21-2-112-21-2-12-12-12-121-21-20000000000000000000000000000000000000000002i−2i−2i2i0000−iii−i
χ7444-4-4-4444-4-4-4-4441-2122-1-1-21-2-112-21-2-12-12-12-121-21-2000000000000000000000000000000000000000000−2i2i2i−2i0000i−i−ii
χ7544-4-4-4444-4-4-4-444-21-2-1-1221-212-2-11-212-12-12-12-1-21-21000000000000000000000000000000000000002-2-220000-111-10000
χ7644-4-4-4444-4-4-4-444-21-2-1-1221-212-2-11-212-12-12-12-1-21-2100000000000000000000000000000000000000-222-200001-1-110000
χ77888888-4-4-4-4-4-4-4-42-42-4-422-4-1222-4-4-12-12-12-12-12-12-12000000000000000000000000000000000000000000000000000000
χ78888888-4-4-4-4-4-4-4-4-42-422-4-422-1-4-4222-12-12-12-12-12-12-1000000000000000000000000000000000000000000000000000000
χ798888-8-8-4-4-4-444442-42-4-422-4-12-2-244-12-12-121-21-21-21-2000000000000000000000000000000000000000000000000000000
χ808888-8-8-4-4-4-44444-42-422-4-422-144-2-22-12-12-1-21-21-21-21000000000000000000000000000000000000000000000000000000
χ8188-8-88-8-4-444-4-4442-4244-2-2-4-122-2-44-121-21-2-12-121-21-2000000000000000000000000000000000000000000000000000000
χ8288-8-88-8-4-444-4-444-42-4-2-24422-1-442-22-1-21-212-12-1-21-21000000000000000000000000000000000000000000000000000000
χ8388-8-8-88-4-44444-4-42-4244-2-2-4-12-224-4-121-21-21-21-2-12-12000000000000000000000000000000000000000000000000000000
χ8488-8-8-88-4-44444-4-4-42-4-2-24422-14-4-222-1-21-21-21-212-12-1000000000000000000000000000000000000000000000000000000
χ858-88-8008-88-800002-4-2-442-242-40000-242-4-2400000000000000000000000000000000000000000000000000000000000000
χ868-88-8008-88-80000-4242-2-44-2-4200004-2-424-200000000000000000000000000000000000000000000000000000000000000
χ878-88-800-44-44−4i34i3−4i34i32-4-2-442-24-1200001-2-121-2−i32i3i3−2i3−i32i3i3−2i3000000000000000000000000000000000000000000000000000000
χ888-88-800-44-44−4i34i3−4i34i3-4242-2-44-22-10000-212-1-212i3−i3−2i3i32i3−i3−2i3i3000000000000000000000000000000000000000000000000000000
χ898-88-800-44-444i3−4i34i3−4i32-4-2-442-24-1200001-2-121-2i3−2i3−i32i3i3−2i3−i32i3000000000000000000000000000000000000000000000000000000
χ908-88-800-44-444i3−4i34i3−4i3-4242-2-44-22-10000-212-1-21−2i3i32i3−i3−2i3i32i3−i3000000000000000000000000000000000000000000000000000000
χ918-8-88008-8-8800002-4-24-4-2242-40000-24-242-400000000000000000000000000000000000000000000000000000000000000
χ928-8-88008-8-880000-424-224-4-2-4200004-24-2-4200000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-444-4−4i34i34i3−4i32-4-24-4-224-1200001-21-2-12−i32i3i3−2i3i3−2i3−i32i3000000000000000000000000000000000000000000000000000000
χ948-8-8800-444-4−4i34i34i3−4i3-424-224-4-22-10000-21-212-12i3−i3−2i3i3−2i3i32i3−i3000000000000000000000000000000000000000000000000000000
χ958-8-8800-444-44i3−4i3−4i34i32-4-24-4-224-1200001-21-2-12i3−2i3−i32i3−i32i3i3−2i3000000000000000000000000000000000000000000000000000000
χ968-8-8800-444-44i3−4i3−4i34i3-424-224-4-22-10000-21-212-1−2i3i32i3−i32i3−i3−2i3i3000000000000000000000000000000000000000000000000000000

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