Finite Group Databasebeta

← Group #11723579

Character table — Group #11723579

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222222222444444444444444444444466666666668888888888888121212121212121212121212123636363672108108
order1233333466666333346666121212121212121212121212122466666666121212121212121212121212124121212121212121212121212282424648
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-111111111-1-1-1-1-1-1-1-111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-111-1
χ611111111111111111-111111111-1-1-1-1-1-1-1-111111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-11
χ711111111111111111-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-11-11
χ811111111111111111-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111111111-1111-11-1
χ92222222-222222222202222-2-2-2-200000000-22-2222222220-2-2-2-2000000000-2-2-2-2000000000000000
χ102222222-222222222202222-2-2-2-200000000-2-22-2-2-2-2-2-2-2-20-2-2-2-20000000002222000000000000000
χ11222222-12-12222-1-1-1-12-1-1-1-1222222222222-10000000000-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000022-1-1-100
χ12222222-12-12222-1-1-1-12-1-1-1-1222222222222-10000000000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-211100
χ13222222-12-12222-1-1-1-1-2-1-1-1-12222-2-2-2-2-2-2-2-2-100000000001-1-1-1-11111111100000000000002-211-100
χ14222222-12-12222-1-1-1-1-2-1-1-1-12222-2-2-2-2-2-2-2-2-100000000001-1-1-1-1111111110000000000000-22-1-1100
χ15222-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122222-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-10000000
χ16222-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-12-2-2-2-211111122-1-1-122-1-1-1-1-1-1-2-2111-2-21111110000000
χ17222-1-1-12222-1-1-12-1-1-1-22-1-1-12-1-1-1-2-211111122222-1-1-1-1-1-1-22-1-1-1-2-2111111-22-1-1-1-2-21111110000000
χ18222-1-1-12222-1-1-12-1-1-1-22-1-1-12-1-1-1-2-21111112-2-2-2-2111111-22-1-1-1-2-21111112-211122-1-1-1-1-1-10000000
χ19222-1-1-12-222-1-1-12-1-1-102-1-1-1-211100−i3−i3−i3i3i3i3-22-222-1-1-1-1-1-10-211100−i3−i3−i3i3i3i30-211100−i3−i3−i3i3i3i30000000
χ20222-1-1-12-222-1-1-12-1-1-102-1-1-1-211100−i3−i3−i3i3i3i3-2-22-2-21111110-211100−i3−i3−i3i3i3i302-1-1-100i3i3i3−i3−i3−i30000000
χ21222-1-1-12-222-1-1-12-1-1-102-1-1-1-211100i3i3i3−i3−i3−i3-22-222-1-1-1-1-1-10-211100i3i3i3−i3−i3−i30-211100i3i3i3−i3−i3−i30000000
χ22222-1-1-12-222-1-1-12-1-1-102-1-1-1-211100i3i3i3−i3−i3−i3-2-22-2-21111110-211100i3i3i3−i3−i3−i302-1-1-100−i3−i3−i3i3i3i30000000
χ2322-12-1-1222-12-1-1-12-1-12-12-1-1-12-1-1-1-12-1-12-1-1222-1-122-1-1-1-12-12-1-1-1-12-1-12-1-12-12-1-1-1-12-1-12-1-10000000
χ2422-12-1-1222-12-1-1-12-1-12-12-1-1-12-1-1-1-12-1-12-1-12-2-211-2-211112-12-1-1-1-12-1-12-1-1-21-21111-211-2110000000
χ2522-12-1-1222-12-1-1-12-1-1-2-12-1-1-12-1-111-211-211222-1-122-1-1-1-1-2-12-1-111-211-211-2-12-1-111-211-2110000000
χ2622-12-1-1222-12-1-1-12-1-1-2-12-1-1-12-1-111-211-2112-2-211-2-21111-2-12-1-111-211-21121-211-1-12-1-12-1-10000000
χ2722-12-1-12-22-12-1-1-12-1-10-12-1-11-211−i3i30−i3i30−i3i3-22-2-1-122-1-1-1-101-211−i3i30−i3i30−i3i301-211−i3i30−i3i30−i3i30000000
χ2822-12-1-12-22-12-1-1-12-1-10-12-1-11-211−i3i30−i3i30−i3i3-2-2211-2-2111101-211−i3i30−i3i30−i3i30-12-1-1i3−i30i3−i30i3−i30000000
χ2922-12-1-12-22-12-1-1-12-1-10-12-1-11-211i3−i30i3−i30i3−i3-22-2-1-122-1-1-1-101-211i3−i30i3−i30i3−i301-211i3−i30i3−i30i3−i30000000
χ3022-12-1-12-22-12-1-1-12-1-10-12-1-11-211i3−i30i3−i30i3−i3-2-2211-2-2111101-211i3−i30i3−i30i3−i30-12-1-1−i3i30−i3i30−i3i30000000
χ3122-1-12-1222-1-12-1-1-12-12-1-12-1-1-12-1-1-1-12-1-1-12222-1-1-1-122-1-12-1-12-1-1-1-12-1-1-122-1-12-1-1-1-12-1-1-120000000
χ3222-1-12-1222-1-12-1-1-12-12-1-12-1-1-12-1-1-1-12-1-1-122-2-21111-2-2112-1-12-1-1-1-12-1-1-12-211-21111-2111-20000000
χ3322-1-12-1222-1-12-1-1-12-1-2-1-12-1-1-12-1111-2111-2222-1-1-1-122-1-1-2-1-12-1111-2111-2-2-1-12-1111-2111-20000000
χ3422-1-12-1222-1-12-1-1-12-1-2-1-12-1-1-12-1111-2111-22-2-21111-2-211-2-1-12-1111-2111-2211-21-1-1-12-1-1-120000000
χ3522-1-12-12-22-1-12-1-1-12-10-1-12-111-21−i3i3i30−i3−i3i30-22-2-1-1-1-122-1-1011-21−i3i3i30−i3−i3i30011-21−i3i3i30−i3−i3i300000000
χ3622-1-12-12-22-1-12-1-1-12-10-1-12-111-21−i3i3i30−i3−i3i30-2-221111-2-211011-21−i3i3i30−i3−i3i300-1-12-1i3−i3−i30i3i3−i300000000
χ3722-1-12-12-22-1-12-1-1-12-10-1-12-111-21i3−i3−i30i3i3−i30-22-2-1-1-1-122-1-1011-21i3−i3−i30i3i3−i30011-21i3−i3−i30i3i3−i300000000
χ3822-1-12-12-22-1-12-1-1-12-10-1-12-111-21i3−i3−i30i3i3−i30-2-221111-2-211011-21i3−i3−i30i3i3−i300-1-12-1−i3i3i30−i3−i3i300000000
χ3922-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-12-1-1-1-12-12-1222-1-1-1-1-1-1222-1-1-12-1-1-1-12-12-12-1-1-12-1-1-1-12-12-10000000
χ4022-1-1-12222-1-1-12-1-1-122-1-1-12-1-1-12-1-1-1-12-12-12-2-2111111-2-22-1-1-12-1-1-1-12-12-1-2111-21111-21-210000000
χ4122-1-1-12222-1-1-12-1-1-12-2-1-1-12-1-1-121111-21-21222-1-1-1-1-1-122-2-1-1-121111-21-21-2-1-1-121111-21-210000000
χ4222-1-1-12222-1-1-12-1-1-12-2-1-1-12-1-1-121111-21-212-2-2111111-2-2-2-1-1-121111-21-212111-2-1-1-1-12-12-10000000
χ4322-1-1-122-22-1-1-12-1-1-120-1-1-12111-2−i3i3−i3i30i30−i3-22-2-1-1-1-1-1-1220111-2−i3i3−i3i30i30−i30111-2−i3i3−i3i30i30−i30000000
χ4422-1-1-122-22-1-1-12-1-1-120-1-1-12111-2−i3i3−i3i30i30−i3-2-22111111-2-20111-2−i3i3−i3i30i30−i30-1-1-12i3−i3i3−i30−i30i30000000
χ4522-1-1-122-22-1-1-12-1-1-120-1-1-12111-2i3−i3i3−i30−i30i3-22-2-1-1-1-1-1-1220111-2i3−i3i3−i30−i30i30111-2i3−i3i3−i30−i30i30000000
χ4622-1-1-122-22-1-1-12-1-1-120-1-1-12111-2i3−i3i3−i30−i30i3-2-22111111-2-20111-2i3−i3i3−i30−i30i30-1-1-12−i3i3−i3i30i30−i30000000
χ47444444-2-4-24444-2-2-2-20-2-2-2-2-4-4-4-40000000020000000000022220000000000000000000000000000
χ48444-2-2-2-24-24-2-2-2-21114-21114-2-2-244-2-2-2-2-2-2-20000000000-2-2111-2-211111100000000000000000000
χ49444-2-2-2-24-24-2-2-2-2111-4-21114-2-2-2-4-4222222-200000000002-211122-1-1-1-1-1-100000000000000000000
χ50444-2-2-2-2-4-24-2-2-2-21110-2111-422200−2i3−2i3−2i32i32i32i32000000000002-1-1-100i3i3i3−i3−i3−i300000000000000000000
χ51444-2-2-2-2-4-24-2-2-2-21110-2111-4222002i32i32i3−2i3−2i3−2i32000000000002-1-1-100−i3−i3−i3i3i3i300000000000000000000
χ5244-24-2-2-24-2-24-2-21-21141-211-24-2-2-2-24-2-24-2-2-20000000000-21-21111-211-21100000000000000000000
χ5344-24-2-2-24-2-24-2-21-211-41-211-24-2-222-422-422-2000000000021-211-1-12-1-12-1-100000000000000000000
χ5444-24-2-2-2-4-2-24-2-21-21101-2112-422−2i32i30−2i32i30−2i32i3200000000000-12-1-1i3−i30i3−i30i3−i300000000000000000000
χ5544-24-2-2-2-4-2-24-2-21-21101-2112-4222i3−2i302i3−2i302i3−2i3200000000000-12-1-1−i3i30−i3i30−i3i300000000000000000000
χ5644-2-24-2-24-2-2-24-211-21411-21-2-24-2-2-2-24-2-2-24-20000000000-211-21111-2111-200000000000000000000
χ5744-2-24-2-24-2-2-24-211-21-411-21-2-24-2222-4222-4-20000000000211-21-1-1-12-1-1-1200000000000000000000
χ5844-2-24-2-2-4-2-2-24-211-21011-2122-42−2i32i32i30−2i3−2i32i30200000000000-1-12-1i3−i3−i30i3i3−i3000000000000000000000
χ5944-2-24-2-2-4-2-2-24-211-21011-2122-422i3−2i3−2i302i32i3−2i30200000000000-1-12-1−i3i3i30−i3−i3i3000000000000000000000
χ6044-2-2-24-24-2-2-2-24111-24111-2-2-2-24-2-2-2-24-24-2-20000000000-2111-21111-21-2100000000000000000000
χ6144-2-2-24-24-2-2-2-24111-2-4111-2-2-2-242222-42-42-200000000002111-2-1-1-1-12-12-100000000000000000000
χ6244-2-2-24-2-4-2-2-2-24111-20111-2222-4−2i32i3−2i32i302i30−2i3200000000000-1-1-12i3−i3i3−i30−i30i300000000000000000000
χ6344-2-2-24-2-4-2-2-2-24111-20111-2222-42i3−2i32i3−2i30−2i302i3200000000000-1-1-12−i3i3−i3i30i30−i300000000000000000000
χ644-4444440-4-4-4-4-444440-4-4-4-400000000000000000000000000000000000000000000000000000000
χ654-44444-202-4-4-4-4-2-2-2-2022220000000000000000000000000000000000000000000000000006−6000
χ664-44444-202-4-4-4-4-2-2-2-202222000000000000000000000000000000000000000000000000000−66000
χ674-44-2-2-240-4-42224-2-2-20-422200000000000000000−2i32i3−2i32i3−2i32i3000000000000000000000000000000000
χ684-44-2-2-240-4-42224-2-2-20-4222000000000000000002i3−2i32i3−2i32i3−2i3000000000000000000000000000000000
χ694-4-24-2-240-42-422-24-2-202-422000000000000000−2i32i300−2i32i32i3−2i3000000000000000000000000000000000
χ704-4-24-2-240-42-422-24-2-202-4220000000000000002i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000
χ714-4-2-24-240-422-42-2-24-2022-42000000000000000−2i32i32i3−2i300−2i32i3000000000000000000000000000000000
χ724-4-2-24-240-422-42-2-24-2022-420000000000000002i3−2i3−2i32i3002i3−2i3000000000000000000000000000000000
χ734-4-2-2-2440-4222-4-2-2-240222-4000000000000000−2i32i3−2i32i32i3−2i300000000000000000000000000000000000
χ744-4-2-2-2440-4222-4-2-2-240222-40000000000000002i3−2i32i3−2i3−2i32i300000000000000000000000000000000000
χ758-88-4-4-4-404-8444-422204-2-2-200000000000000000000000000000000000000000000000000000000
χ768-8-48-4-4-4044-8442-4220-24-2-200000000000000000000000000000000000000000000000000000000
χ778-8-4-48-4-40444-8422-420-2-24-200000000000000000000000000000000000000000000000000000000
χ788-8-4-4-48-404444-8222-40-2-2-2400000000000000000000000000000000000000000000000000000000

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