Finite Group Databasebeta

← Group #13164613

Character table — Group #13164613

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1236666691212242427363612366666912122424273636246121212121218242448485472722461212121212182424484854727224612121212121824244848547272
order13236666233332662626666626666266262666662666626626266666266662664124121212121241212121241212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ3111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ411111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-1
χ511111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ611111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ7222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000
χ8222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000
χ9222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000
χ1033-13-1-1-1-130000-10033-13-1-1-1-130000-10033-13-1-1-1-130000-10033-13-1-1-1-130000-10033-13-1-1-1-130000-100
χ1133-13-1-1-1-1-3000010033-13-1-1-1-1-3000010033-13-1-1-1-1-3000010033-13-1-1-1-1-3000010033-13-1-1-1-1-30000100
χ1266-2-3-21110000000066-2-3-21110000000066-2-3-21110000000066-2-3-21110000000066-2-3-211100000000
χ136-360-3000000000006-360-3000000000006-360-3000000000006-360-3000000000006-360-300000000000
χ146-3-2014-2-2000000006-3-2014-2-2000000006-3-2014-2-2000000006-3-2014-2-2000000006-3-2014-2-200000000
χ156-3-201-24-2000000006-3-201-24-2000000006-3-201-24-2000000006-3-201-24-2000000006-3-201-24-200000000
χ166-3-201-2-24000000006-3-201-2-24000000006-3-201-2-24000000006-3-201-2-24000000006-3-201-2-2400000000
χ17111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ18111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32
χ19111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32
χ2011111111-11111-1-1-111111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111
χ2111111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32
χ2211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32
χ23222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000-2-2-21-21110-2-211000-2-2-21-21110-2-211000
χ24222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000-2-2-21-211101−i31+i3−1+i32−1−i32000-2-2-21-211101−i31+i3−1+i32−1−i32000
χ25222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000-2-2-21-211101+i31−i3−1−i32−1+i32000-2-2-21-211101+i31−i3−1−i32−1+i32000
χ2633-13-1-1-1-130000-10033-13-1-1-1-130000-10033-13-1-1-1-130000-100-3-31-31111-30000100-3-31-31111-30000100
χ2733-13-1-1-1-1-3000010033-13-1-1-1-1-3000010033-13-1-1-1-1-30000100-3-31-3111130000-100-3-31-3111130000-100
χ2866-2-3-21110000000066-2-3-21110000000066-2-3-211100000000-6-6232-1-1-100000000-6-6232-1-1-100000000
χ296-360-3000000000006-360-3000000000006-360-300000000000-63-60300000000000-63-60300000000000
χ306-3-2014-2-2000000006-3-2014-2-2000000006-3-2014-2-200000000-6320-1-42200000000-6320-1-42200000000
χ316-3-201-24-2000000006-3-201-24-2000000006-3-201-24-200000000-6320-12-4200000000-6320-12-4200000000
χ326-3-201-2-24000000006-3-201-2-24000000006-3-201-2-2400000000-6320-122-400000000-6320-122-400000000
χ3311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ34111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32
χ35111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32
χ3611111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ3711111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32
χ3811111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32
χ39222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000-2-2-21-21110-2-211000222-12-1-1-1022-1-1000-2-2-21-21110-2-211000
χ40222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000-2-2-21-211101−i31+i3−1+i32−1−i32000222-12-1-1-10−1+i3−1−i31−i321+i32000-2-2-21-211101−i31+i3−1+i32−1−i32000
χ41222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000-2-2-21-211101+i31−i3−1−i32−1+i32000222-12-1-1-10−1−i3−1+i31+i321−i32000-2-2-21-211101+i31−i3−1−i32−1+i32000
χ4233-13-1-1-1-130000-10033-13-1-1-1-130000-100-3-31-31111-3000010033-13-1-1-1-130000-100-3-31-31111-30000100
χ4333-13-1-1-1-1-3000010033-13-1-1-1-1-30000100-3-31-3111130000-10033-13-1-1-1-1-30000100-3-31-3111130000-100
χ4466-2-3-21110000000066-2-3-211100000000-6-6232-1-1-10000000066-2-3-211100000000-6-6232-1-1-100000000
χ456-360-3000000000006-360-300000000000-63-603000000000006-360-300000000000-63-60300000000000
χ466-3-2014-2-2000000006-3-2014-2-200000000-6320-1-422000000006-3-2014-2-200000000-6320-1-42200000000
χ476-3-201-24-2000000006-3-201-24-200000000-6320-12-42000000006-3-201-24-200000000-6320-12-4200000000
χ486-3-201-2-24000000006-3-201-2-2400000000-6320-122-4000000006-3-201-2-2400000000-6320-122-400000000
χ4911111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ50111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32-1-1-1-1-1-1-1-1-11−i321+i321−i321+i32-11−i321+i32111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ51111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32-1-1-1-1-1-1-1-1-11+i321−i321+i321−i32-11+i321−i32111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ5211111111-11111-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111111-11111-1-1-1
χ5311111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i32-1-1-1-1-1-1-1-111−i321+i321−i321+i321−1+i32−1−i3211111111-1−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ5411111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i32-1-1-1-1-1-1-1-111+i321−i321+i321−i321−1−i32−1+i3211111111-1−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ55222-12-1-1-1022-1-1000222-12-1-1-1022-1-1000-2-2-21-21110-2-211000-2-2-21-21110-2-211000222-12-1-1-1022-1-1000
χ56222-12-1-1-10−1+i3−1−i31−i321+i32000222-12-1-1-10−1+i3−1−i31−i321+i32000-2-2-21-211101−i31+i3−1+i32−1−i32000-2-2-21-211101−i31+i3−1+i32−1−i32000222-12-1-1-10−1+i3−1−i31−i321+i32000
χ57222-12-1-1-10−1−i3−1+i31+i321−i32000222-12-1-1-10−1−i3−1+i31+i321−i32000-2-2-21-211101+i31−i3−1−i32−1+i32000-2-2-21-211101+i31−i3−1−i32−1+i32000222-12-1-1-10−1−i3−1+i31+i321−i32000
χ5833-13-1-1-1-130000-10033-13-1-1-1-130000-100-3-31-31111-30000100-3-31-31111-3000010033-13-1-1-1-130000-100
χ5933-13-1-1-1-1-3000010033-13-1-1-1-1-30000100-3-31-3111130000-100-3-31-3111130000-10033-13-1-1-1-1-30000100
χ6066-2-3-21110000000066-2-3-211100000000-6-6232-1-1-100000000-6-6232-1-1-10000000066-2-3-211100000000
χ616-360-3000000000006-360-300000000000-63-60300000000000-63-603000000000006-360-300000000000
χ626-3-2014-2-2000000006-3-2014-2-200000000-6320-1-42200000000-6320-1-422000000006-3-2014-2-200000000
χ636-3-201-24-2000000006-3-201-24-200000000-6320-12-4200000000-6320-12-42000000006-3-201-24-200000000
χ646-3-201-2-24000000006-3-201-2-2400000000-6320-122-400000000-6320-122-4000000006-3-201-2-2400000000
χ652222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ66222222222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3-2-2-2-2-2-2-2-2-21−i31+i31−i31+i3-21−i31+i3000000000000000000000000000000000000000000000000
χ67222222222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3-2-2-2-2-2-2-2-2-21+i31−i31+i31−i3-21+i31−i3000000000000000000000000000000000000000000000000
χ6822222222-22222-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2222000000000000000000000000000000000000000000000000
χ6922222222-2−1+i3−1−i3−1+i3−1−i3-21−i31+i3-2-2-2-2-2-2-2-221−i31+i31−i31+i32−1+i3−1−i3000000000000000000000000000000000000000000000000
χ7022222222-2−1−i3−1+i3−1−i3−1+i3-21+i31−i3-2-2-2-2-2-2-2-221+i31−i31+i31−i32−1−i3−1+i3000000000000000000000000000000000000000000000000
χ71444-24-2-2-2044-2-2000-4-4-42-42220-4-422000000000000000000000000000000000000000000000000000
χ72444-24-2-2-20−2+2i3−2−2i31−i31+i3000-4-4-42-422202−2i32+2i3−1+i3−1−i3000000000000000000000000000000000000000000000000000
χ73444-24-2-2-20−2−2i3−2+2i31+i31−i3000-4-4-42-422202+2i32−2i3−1−i3−1+i3000000000000000000000000000000000000000000000000000
χ7466-26-2-2-2-260000-200-6-62-62222-60000200000000000000000000000000000000000000000000000000
χ7566-26-2-2-2-2-60000200-6-62-6222260000-200000000000000000000000000000000000000000000000000
χ761212-4-6-422200000000-12-12464-2-2-200000000000000000000000000000000000000000000000000000000
χ7712-6120-600000000000-126-120600000000000000000000000000000000000000000000000000000000000
χ7812-6-4028-4-400000000-12640-2-84400000000000000000000000000000000000000000000000000000000
χ7912-6-402-48-400000000-12640-24-8400000000000000000000000000000000000000000000000000000000
χ8012-6-402-4-4800000000-12640-244-800000000000000000000000000000000000000000000000000000000

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