Finite Group Databasebeta

← Group #13147219

Character table — Group #13147219

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222226666666666121212121212121212121212121212121212121212121212121818181824242424242424242424242424242424242424247272727272727272108108
order122234466612121212344666121212123346666661212121212121212121212121212121222443366666612121212121212121212121266661212121224
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211
χ4111111111111111111111111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1
χ5111111111111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211
χ6111111111111111111111111−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1
χ711111-1-1111-1-1-1-1111111-1-1-1-111-111111111-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11
χ811111-1-1111-1-1-1-1111111-1-1-1-111-111111111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1
χ911111-1-1111-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11
χ1011111-1-1111-1-1-1-1111111-1-1-1-1−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1
χ1111111-1-1111-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11
χ1211111-1-1111-1-1-1-1111111-1-1-1-1−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1
χ1322222222222222-122-1-1-1-1-1-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ1422222222222222-122-1-1-1-1-1-1-1−1−i3−1+i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i321+i321+i321−i321−i321+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321−i321−i321−i321−i320000000000
χ1522222222222222-122-1-1-1-1-1-1-1−1+i3−1−i32−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i321−i321−i321+i321+i321−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321+i321+i321+i321+i320000000000
χ1622222-2-2222-2-2-2-2-122-1-1-1111122-222222222-2-2-1-1-1-1-1-11111110000-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ1722222-2-2222-2-2-2-2-122-1-1-11111−1−i3−1+i3-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i321+i321−i321−i321+i321−i321+i31+i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i320000000000
χ1822222-2-2222-2-2-2-2-122-1-1-11111−1+i3−1−i3-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i321−i321+i321+i321−i321+i321−i31−i31+i31+i3−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i320000000000
χ192-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i-1-10-1-1111100000000000000002-22i−2i-1-11-11-111i−ii−iii−i−iii−i−i1-11-1i−ii−i00
χ202-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i-1-10-1-111110000000000000000-22−2i2i-1-11-11-111i−ii−iii−i−iii−i−i-11-11−ii−ii00
χ212-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i1+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1+i3200000000000000002-22i−2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ700
χ222-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i1+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000-22−2i2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ700
χ232-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i1−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1−i3200000000000000002-22i−2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i32ζ7−ζ7ζ11−ζ1100
χ242-22-222i−2i-22-22i2i−2i−2i200-22-22i2i−2i−2i1−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1−i320000000000000000-22−2i2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ1100
χ252-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i-1-10-1-1111100000000000000002-2−2i2i-1-11-11-111−ii−ii−i−iii−i−iii1-11-1−ii−ii00
χ262-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i-1-10-1-111110000000000000000-222i−2i-1-11-11-111−ii−ii−i−iii−i−iii-11-11i−ii−i00
χ272-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i1+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1+i3200000000000000002-2−2i2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ700
χ282-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i1+i321−i3201+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000-222i−2i1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ71+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ700
χ292-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i1−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1−i3200000000000000002-2−2i2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ1100
χ302-22-22−2i2i-22-2−2i−2i2i2i200-22-2−2i−2i2i2i1−i321+i3201−i321+i32−1+i32−1−i32−1+i32−1−i320000000000000000-222i−2i1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ111−i32−1+i321+i32−1−i32ζ7−ζ7ζ11−ζ1100
χ312-2-22200-2-22000022-2-2-220000220-2-2-2-2222-200222-2-2-20000000000222-22-2-2-20000000000000000000000
χ322-2-22200-2-22000022-2-2-220000−1−i3−1+i301+i31−i31+i31−i3−1−i3−1+i32-200222-2-2-20000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000000000
χ332-2-22200-2-22000022-2-2-220000−1+i3−1−i301−i31+i31−i31+i3−1+i3−1−i32-200222-2-2-20000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000000000
χ342-2-22200-2-220000-12-211-13−33−3220-2-2-2-2222-200-1-1-1111333−3−3−30000-1-1-11-111100003−33−33−33−30000000000
χ352-2-22200-2-220000-12-211-13−33−3−1−i3−1+i301+i31−i31+i31−i3−1−i3−1+i32-200-1-1-1111333−3−3−300001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i3200002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ110000000000
χ362-2-22200-2-220000-12-211-13−33−3−1+i3−1−i301−i31+i31−i31+i3−1+i3−1−i32-200-1-1-1111333−3−3−300001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ110000000000
χ372-2-22200-2-220000-12-211-1−33−33220-2-2-2-2222-200-1-1-1111−3−3−33330000-1-1-11-11110000−33−33−33−330000000000
χ382-2-22200-2-220000-12-211-1−33−33−1−i3−1+i301+i31−i31+i31−i3−1−i3−1+i32-200-1-1-1111−3−3−333300001+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i320000−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ110000000000
χ392-2-22200-2-220000-12-211-1−33−33−1+i3−1−i301−i31+i31−i31+i3−1+i3−1−i32-200-1-1-1111−3−3−333300001−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i320000ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ110000000000
χ40333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000000000000000-1-1
χ41333333333333333-1-1333333300-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3000000000000000000000000000011
χ4233333-3-3333-3-3-3-33-1-1333-3-3-3-3001000000-1-111-1-1-1-1-1-111111133-3-300000000000000000000000000001-1
χ4333333-3-3333-3-3-3-33-1-1333-3-3-3-3001000000-1-111-1-1-1-1-1-1111111-3-3330000000000000000000000000000-11
χ4444-4-44004-4-400004004-4-40000-2-2022-2-22200000000000000000000-2-22222-2-20000000000000000000000
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χ5044-4-44004-4-40000-200-2222i3−2i3−2i32i3-2-2022-2-2220000000000000000000011-1-1-1-1110000i3−i3−i3i3i3−i3−i3i30000000000
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χ554-44-444i−4i-44-44i4i−4i−4i-2002-22−2i−2i2i2i1−i31+i301−i31+i3−1+i3−1−i3−1+i3−1−i300000000000000000000−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i322ζ7−2ζ72ζ11−2ζ11−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ110000000000
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χ726-6-66-30033-333−3333−3306-60000000000000000-3333−330000000000000000000000000000000000000000000000
χ736-6-66-30033-333−3333−330-2200000000000000001-1−334-2-2-422023−230−23230000000000000000000000000000000000
χ746-6-66-30033-333−3333−330-2200000000000000001-1−33-24-22-42−23023230−230000000000000000000000000000000000
χ756-6-66-30033-333−3333−330-2200000000000000001-1−33-2-2422-423−230−232300000000000000000000000000000000000
χ766-6-66-30033-3−3333−333306-60000000000000000-33−33330000000000000000000000000000000000000000000000
χ776-6-66-30033-3−3333−33330-2200000000000000001-13−34-2-2-4220−2323023−230000000000000000000000000000000000
χ786-6-66-30033-3−3333−33330-2200000000000000001-13−3-24-22-42230−23−230230000000000000000000000000000000000
χ796-6-66-30033-3−3333−33330-2200000000000000001-13−3-2-2422-4−2323023−2300000000000000000000000000000000000
χ801212-12-12-600-666−6i36i36i3−6i3000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-600-6666i3−6i3−6i36i3000000000000000000000000000000000000000000000000000000000000000000000
χ8212-1212-12-612i−12i6-66−6i−6i6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-6−12i12i6-666i6i−6i−6i000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.