Finite Group Databasebeta

← Group #72254060

Character table — Group #72254060

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1222224444666699912121212121212121212121212121212181818181818181818181818181827272736363636363636365454545454545454545454548181162162162243243243
order133333333333392333339999999999999333333336666992669999999966666666666666181818266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-11111111111-111111111111-1-1-1-1-1-1-1-1
χ3111111111111111−1+i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ4111111111111111−1+i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32-1−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i32
χ5111111111111111−1−i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ6111111111111111−1−i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32-1−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i32
χ711111111111111-111111111111111111111111111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ811111111111111-111111111111111111111111111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ911111111111111-1−1+i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1−i3211−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ1011111111111111-1−1+i32−1−i321111111111111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1−i32-11−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32-11−i321+i321−1+i32−1−i32
χ1111111111111111-1−1−i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1+i3211+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ1211111111111111-1−1−i32−1+i321111111111111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1+i32-11+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321−i32-11+i321−i321−1−i32−1+i32
χ132222222222222-1022222-1-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1200-1-1-1-1-1-1-1-120000000000022-1-1-1000
χ142222222222222-1022222-1-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1-200-1-1-1-1-1-1-1-1-200000000000-2-2111000
χ152222222222222-10−1+i3−1−i3222-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i300001−i321+i322001−i321−i321−i321−i321+i321+i321+i321+i32200000000000−1+i3−1−i3-11−i321+i32000
χ162222222222222-10−1+i3−1−i3222-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i300001−i321+i32-2001−i321−i321−i321−i321+i321+i321+i321+i32-2000000000001−i31+i31−1+i32−1−i32000
χ172222222222222-10−1−i3−1+i3222-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i300001+i321−i322001+i321+i321+i321+i321−i321−i321−i321−i32200000000000−1−i3−1+i3-11+i321−i32000
χ182222222222222-10−1−i3−1+i3222-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i300001+i321−i32-2001+i321+i321+i321+i321−i321−i321−i321−i32-2000000000001+i31−i31−1−i32−1+i32000
χ192222222222-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-12-1-1-12-1-1-12222220222-1-1-12-1-1-10-1-1-12-1-1-12-1-1-100000000
χ202222222222-1-1-122−1+i3−1−i3-1-1-12222-1-1-1-1-1-1-1-1-1−1+i31−i321−i321−i32−1−i31+i321+i321+i322222−1+i3−1−i30−1+i3−1−i3−1+i31−i321−i321−i32−1−i31+i321+i321+i320-1-1-1−1+i31−i321−i321−i32−1−i31+i321+i321+i3200000000
χ212222222222-1-1-122−1−i3−1+i3-1-1-12222-1-1-1-1-1-1-1-1-1−1−i31+i321+i321+i32−1+i31−i321−i321−i322222−1−i3−1+i30−1−i3−1+i3−1−i31+i321+i321+i32−1+i31−i321−i321−i320-1-1-1−1−i31+i321+i321+i32−1+i31−i321−i321−i3200000000
χ222222222222-1-1-12-222-1-1-12222-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-2-2-2-2220-2-22-1-1-12-1-1-10111-2111-211100000000
χ232222222222-1-1-12-2−1+i3−1−i3-1-1-12222-1-1-1-1-1-1-1-1-1−1+i31−i321−i321−i32−1−i31+i321+i321+i32-2-2-2-2−1+i3−1−i301−i31+i3−1+i31−i321−i321−i32−1−i31+i321+i321+i3201111−i3−1+i32−1+i32−1+i321+i3−1−i32−1−i32−1−i3200000000
χ242222222222-1-1-12-2−1−i3−1+i3-1-1-12222-1-1-1-1-1-1-1-1-1−1−i31+i321+i321+i32−1+i31−i321−i321−i32-2-2-2-2−1−i3−1+i301+i31−i3−1−i31+i321+i321+i32−1+i31−i321−i321−i3201111+i3−1−i32−1−i32−1−i321−i3−1+i32−1+i32−1+i3200000000
χ2522-1-1-122-1-1-12-1-122222-1-12-1-1-1222-1-1-1-1-1-1-12-1-1-12-1-12-1-1-122022-12-1-1-12-1-102-1-1-12-1-1-12-1-100000000
χ2622-1-1-122-1-1-12-1-122−1+i3−1−i32-1-12-1-1-1222-1-1-1-1-1-11−i32−1+i31−i321−i321+i32−1−i31+i321+i322-1-1-1−1+i3−1−i30−1+i3−1−i31−i32−1+i31−i321−i321+i32−1−i31+i321+i3202-1-11−i32−1+i31−i321−i321+i32−1−i31+i321+i3200000000
χ2722-1-1-122-1-1-12-1-122−1−i3−1+i32-1-12-1-1-1222-1-1-1-1-1-11+i32−1−i31+i321+i321−i32−1+i31−i321−i322-1-1-1−1−i3−1+i30−1−i3−1+i31+i32−1−i31+i321+i321−i32−1+i31−i321−i3202-1-11+i32−1−i31+i321+i321−i32−1+i31−i321−i3200000000
χ2822-1-1-122-1-1-12-1-12-2222-1-12-1-1-1222-1-1-1-1-1-1-12-1-1-12-1-1-2111220-2-2-12-1-1-12-1-10-2111-2111-21100000000
χ2922-1-1-122-1-1-12-1-12-2−1+i3−1−i32-1-12-1-1-1222-1-1-1-1-1-11−i32−1+i31−i321−i321+i32−1−i31+i321+i32-2111−1+i3−1−i301−i31+i31−i32−1+i31−i321−i321+i32−1−i31+i321+i320-211−1+i321−i3−1+i32−1+i32−1−i321+i3−1−i32−1−i3200000000
χ3022-1-1-122-1-1-12-1-12-2−1−i3−1+i32-1-12-1-1-1222-1-1-1-1-1-11+i32−1−i31+i321+i321−i32−1+i31−i321−i32-2111−1−i3−1+i301+i31−i31+i32−1−i31+i321+i321−i32−1+i31−i321−i320-211−1−i321+i3−1−i32−1−i32−1+i321−i3−1+i32−1+i3200000000
χ3122-1-1-122-1-1-1-12-12222-12-12-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-12-1-1-122022-1-12-1-1-12-10-12-1-1-12-1-1-12-100000000
χ3222-1-1-122-1-1-1-12-122−1+i3−1−i3-12-12-1-1-1-1-1-1222-1-1-11−i321−i32−1+i31−i321+i321+i32−1−i31+i322-1-1-1−1+i3−1−i30−1+i3−1−i31−i321−i32−1+i31−i321+i321+i32−1−i31+i320-12-11−i321−i32−1+i31−i321+i321+i32−1−i31+i3200000000
χ3322-1-1-122-1-1-1-12-122−1−i3−1+i3-12-12-1-1-1-1-1-1222-1-1-11+i321+i32−1−i31+i321−i321−i32−1+i31−i322-1-1-1−1−i3−1+i30−1−i3−1+i31+i321+i32−1−i31+i321−i321−i32−1+i31−i320-12-11+i321+i32−1−i31+i321−i321−i32−1+i31−i3200000000
χ3422-1-1-122-1-1-1-12-12-222-12-12-1-1-1-1-1-1222-1-1-1-1-12-1-1-12-1-2111220-2-2-1-12-1-1-12-101-2111-2111-2100000000
χ3522-1-1-122-1-1-1-12-12-2−1+i3−1−i3-12-12-1-1-1-1-1-1222-1-1-11−i321−i32−1+i31−i321+i321+i32−1−i31+i32-2111−1+i3−1−i301−i31+i31−i321−i32−1+i31−i321+i321+i32−1−i31+i3201-21−1+i32−1+i321−i3−1+i32−1−i32−1−i321+i3−1−i3200000000
χ3622-1-1-122-1-1-1-12-12-2−1−i3−1+i3-12-12-1-1-1-1-1-1222-1-1-11+i321+i32−1−i31+i321−i321−i32−1+i31−i32-2111−1−i3−1+i301+i31−i31+i321+i32−1−i31+i321−i321−i32−1+i31−i3201-21−1−i32−1−i321+i3−1−i32−1+i32−1+i321−i3−1+i3200000000
χ3722-1-1-122-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1222-1-1-12-1-1-122-1-1-122022-1-1-12-1-1-120-1-12-1-1-12-1-1-1200000000
χ3822-1-1-122-1-1-1-1-1222−1+i3−1−i3-1-122-1-1-1-1-1-1-1-1-12221−i321−i321−i32−1+i31+i321+i321+i32−1−i32-1-1-1−1+i3−1−i30−1+i3−1−i31−i321−i321−i32−1+i31+i321+i321+i32−1−i30-1-121−i321−i321−i32−1+i31+i321+i321+i32−1−i300000000
χ3922-1-1-122-1-1-1-1-1222−1−i3−1+i3-1-122-1-1-1-1-1-1-1-1-12221+i321+i321+i32−1−i31−i321−i321−i32−1+i32-1-1-1−1−i3−1+i30−1−i3−1+i31+i321+i321+i32−1−i31−i321−i321−i32−1+i30-1-121+i321+i321+i32−1−i31−i321−i321−i32−1+i300000000
χ4022-1-1-122-1-1-1-1-122-222-1-122-1-1-1-1-1-1-1-1-1222-1-1-12-1-1-12-2111220-2-2-1-1-12-1-1-12011-2111-2111-200000000
χ4122-1-1-122-1-1-1-1-122-2−1+i3−1−i3-1-122-1-1-1-1-1-1-1-1-12221−i321−i321−i32−1+i31+i321+i321+i32−1−i3-2111−1+i3−1−i301−i31+i31−i321−i321−i32−1+i31+i321+i321+i32−1−i3011-2−1+i32−1+i32−1+i321−i3−1−i32−1−i32−1−i321+i300000000
χ4222-1-1-122-1-1-1-1-122-2−1−i3−1+i3-1-122-1-1-1-1-1-1-1-1-12221+i321+i321+i32−1−i31−i321−i321−i32−1+i3-2111−1−i3−1+i301+i31−i31+i321+i321+i32−1−i31−i321−i321−i32−1+i3011-2−1−i32−1−i32−1−i321+i3−1+i32−1+i32−1+i321−i300000000
χ434444444444-2-2-2-2044-2-2-2-2-2-2-21111111114-2-2-24-2-2-20000-2-2000-2111-211100000000000000000000
χ444444444444-2-2-2-20−2+2i3−2−2i3-2-2-2-2-2-2-2111111111−2+2i31−i31−i31−i3−2−2i31+i31+i31+i300001−i31+i30001−i3−1+i32−1+i32−1+i321+i3−1−i32−1−i32−1−i3200000000000000000000
χ454444444444-2-2-2-20−2−2i3−2+2i3-2-2-2-2-2-2-2111111111−2−2i31+i31+i31+i3−2+2i31−i31−i31−i300001+i31−i30001+i3−1−i32−1−i32−1−i321−i3−1+i32−1+i32−1+i3200000000000000000000
χ4644-2-2-244-2-2-24-2-2-20444-2-2-2111-2-2-2111111-24-2-2-24-2-20000-2-20001-2111-21100000000000000000000
χ4744-2-2-244-2-2-24-2-2-20−2+2i3−2−2i34-2-2-2111-2-2-21111111−i3−2+2i31−i31−i31+i3−2−2i31+i31+i300001−i31+i3000−1+i321−i3−1+i32−1+i32−1−i321+i3−1−i32−1−i3200000000000000000000
χ4844-2-2-244-2-2-24-2-2-20−2−2i3−2+2i34-2-2-2111-2-2-21111111+i3−2−2i31+i31+i31−i3−2+2i31−i31−i300001+i31−i3000−1−i321+i3−1−i32−1−i32−1+i321−i3−1+i32−1+i3200000000000000000000
χ4944-2-2-244-2-2-2-24-2-2044-24-2-2111111-2-2-2111-2-24-2-2-24-20000-2-200011-2111-2100000000000000000000
χ5044-2-2-244-2-2-2-24-2-20−2+2i3−2−2i3-24-2-2111111-2-2-21111−i31−i3−2+2i31−i31+i31+i3−2−2i31+i300001−i31+i3000−1+i32−1+i321−i3−1+i32−1−i32−1−i321+i3−1−i3200000000000000000000
χ5144-2-2-244-2-2-2-24-2-20−2−2i3−2+2i3-24-2-2111111-2-2-21111+i31+i3−2−2i31+i31−i31−i3−2+2i31−i300001+i31−i3000−1−i32−1−i321+i3−1−i32−1+i32−1+i321−i3−1+i3200000000000000000000
χ5244-2-2-244-2-2-2-2-24-2044-2-24-2111111111-2-2-2-2-2-24-2-2-240000-2-2000111-2111-200000000000000000000
χ5344-2-2-244-2-2-2-2-24-20−2+2i3−2−2i3-2-24-2111111111-2-2-21−i31−i31−i3−2+2i31+i31+i31+i3−2−2i300001−i31+i3000−1+i32−1+i32−1+i321−i3−1−i32−1−i32−1−i321+i300000000000000000000
χ5444-2-2-244-2-2-2-2-24-20−2−2i3−2+2i3-2-24-2111111111-2-2-21+i31+i31+i3−2−2i31−i31−i31−i3−2+2i300001+i31−i3000−1−i32−1−i32−1−i321+i3−1+i32−1+i32−1+i321−i300000000000000000000
χ5566666-3-3-3-3-36660000-3-3-300000000000000000000000000060000000000-30000000000000000000
χ5666666-3-3-3-3-36660000-3-3-3000000000000000000000000000-6000000000030000000000000000000
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χ606-3-36-36-3-36-30006-600000-3-36-30000000000000000033-63000000000000000000000000000000000
χ616-3-3-366-3-3-360006600000-3-3-3600000000000000000-3-3-36000000000000000000000000000000000
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χ6812-612-6-6-63-633000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000
χ6912-612-6-6-63-633000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ7012-612-6-6-63-633000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ7112-6-612-612-6-612-6000-600000033-63000000000000000000000000000000000000000000000000000000
χ7212-6-612-6-633-63000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ7312-6-612-6-633-63000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000
χ7412-6-612-6-633-63000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ7512-6-6-61212-6-6-612000-6000000333-6000000000000000000000000000000000000000000000000000000
χ7612-6-6-612-6333-6000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ7712-6-6-612-6333-6000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ7812-6-6-612-6333-6000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.