Finite Group Databasebeta

← Group #10695437

Character table — Group #10695437

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222244444444888888888888888816161616161616161616161624242424242424242424242424242424
order1222222222223666666644446666224466661212121212121212444412121212121212122222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-21111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000−i3−i3i3i3−i3−i3i3i30000000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000i3i3−i3−i3i3i3−i3−i30000000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-20000000022-2-20000002-200002-22-20000000000000000
χ2022222222-2-2-2-2222222222-22-2-2-2-2-20000000022-2-2000000-220000-22-220000000000000000
χ2122222222-2-2-2-222222222-22-22-2-2-2-200000000-2-22200002-2002-22-200000000000000000000
χ2222222222-2-2-2-222222222-22-22-2-2-2-200000000-2-2220000-2200-22-2200000000000000000000
χ2322222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3-1-111−i3−i3i3i3002-2−i3i3i3−i3-11-110000000000000000
χ2422222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3-1-111−i3−i3i3i300-22i3−i3−i3i31-11-10000000000000000
χ2522222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3-1-111i3i3−i3−i3002-2i3−i3−i3i3-11-110000000000000000
χ2622222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3-1-111i3i3−i3−i300-22−i3i3i3−i31-11-10000000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i311-1-1i3i3−i3−i32-200-11-11−i3i3i3−i30000000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i311-1-1i3i3−i3−i3-22001-11-1i3−i3−i3i30000000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i311-1-1−i3−i3i3i32-200-11-11i3−i3−i3i30000000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i311-1-1−i3−i3i3i3-22001-11-1−i3i3i3−i30000000000000000
χ312222-2-2-2-22-2-222222-2-2-2-2000022-2-22-2002-22-20000000000000000000000000000−i2−i2i2i2−i2−i2i2i2
χ322222-2-2-2-22-2-222222-2-2-2-2000022-2-22-2002-22-20000000000000000000000000000i2i2−i2−i2i2i2−i2−i2
χ332222-2-2-2-22-2-222222-2-2-2-2000022-2-2-2200-22-220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2
χ342222-2-2-2-22-2-222222-2-2-2-2000022-2-2-2200-22-220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2
χ3522-2-222-2-222-2-222-2-222-2-200002-22-2002i−2i000000002i−2i2i−2i000000000000000000002−22−2−i2i2−i2i2
χ3622-2-222-2-222-2-222-2-222-2-200002-22-2002i−2i000000002i−2i2i−2i00000000000000000000−22−22i2−i2i2−i2
χ3722-2-222-2-222-2-222-2-222-2-200002-22-200−2i2i00000000−2i2i−2i2i000000000000000000002−22−2i2−i2i2−i2
χ3822-2-222-2-222-2-222-2-222-2-200002-22-200−2i2i00000000−2i2i−2i2i00000000000000000000−22−22−i2i2−i2i2
χ3922-2-2-2-2222-22-222-2-2-2-22222-2-22-2-22000000002-22-20000000000000000000000002i−2i−2i2i0000
χ4022-2-2-2-2222-22-222-2-2-2-22222-2-22-2-22000000002-22-2000000000000000000000000−2i2i2i−2i0000
χ4122-2-2-2-2222-22-222-2-2-2-222-2-2222-2-2200000000-22-2200000000000000000000000000002-2-22
χ4222-2-2-2-2222-22-222-2-2-2-222-2-2222-2-2200000000-22-220000000000000000000000000000-222-2
χ4322-2-2-2-222-22-2222-2-2-2-2222-2-22-222-2000000002-2-220000000000000000000022-2-200000000
χ4422-2-2-2-222-22-2222-2-2-2-2222-2-22-222-2000000002-2-2200000000000000000000-2-22200000000
χ4522-2-2-2-222-22-2222-2-2-2-222-222-2-222-200000000-222-2000000000000000022-2-2000000000000
χ4622-2-2-2-222-22-2222-2-2-2-222-222-2-222-200000000-222-20000000000000000-2-222000000000000
χ474444-4-4-4-44-4-44-2-2-2-222220000-2-2224-400-22-22000000000000000000000000000000000000
χ484444-4-4-4-44-4-44-2-2-2-222220000-2-222-44002-22-2000000000000000000000000000000000000
χ494444-4-4-4-4-444-44444-4-4-4-40000-4-44400000000000000000000000000000000000000000000
χ504444-4-4-4-4-444-4-2-2-2-22222000022-2-20000−2i32i32i3−2i3000000000000000000000000000000000000
χ514444-4-4-4-4-444-4-2-2-2-22222000022-2-200002i3−2i3−2i32i3000000000000000000000000000000000000
χ5244-4-444-4-444-4-4-2-222-2-2220000-22-22004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ5344-4-444-4-444-4-4-2-222-2-2220000-22-2200−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ5444-4-444-4-4-4-44444-4-444-4-40000-44-4400000000000000000000000000000000000000000000
χ5544-4-444-4-4-4-444-2-222-2-22200002-22-200000000000023−23−23230000000000000000000000000000
χ5644-4-444-4-4-4-444-2-222-2-22200002-22-2000000000000−232323−230000000000000000000000000000
χ5744-4-4-4-4444-44-4-2-22222-2-244-4-4-222-200000000-22-2200000000000000000000000000000000
χ5844-4-4-4-4444-44-4-2-22222-2-2-4-444-222-2000000002-22-200000000000000000000000000000000
χ5944-4-4-4-444-44-44-2-22222-2-24-4-442-2-2200000000-222-200000000000000000000000000000000
χ6044-4-4-4-444-44-44-2-22222-2-2-444-42-2-22000000002-2-2200000000000000000000000000000000
χ614-44-44-44-400004-44-44-44-40000000000000000000000000000000000002-22-2000000000000
χ624-44-44-44-400004-44-44-44-4000000000000000000000000000000000000-22-22000000000000
χ634-44-4-44-4400004-44-4-44-4400000000000000000000000000000000000000002-22-200000000
χ644-44-4-44-4400004-44-4-44-440000000000000000000000000000000000000000-22-2200000000
χ654-4-444-4-4400004-4-444-4-4400000000000000000000000000000000000000002-2-2200000000
χ664-4-444-4-4400004-4-444-4-440000000000000000000000000000000000000000-222-200000000
χ674-4-44-444-400004-4-44-444-40000000000000000000000000000000000002-2-22000000000000
χ684-4-44-444-400004-4-44-444-4000000000000000000000000000000000000-222-2000000000000
χ698-88-88-88-80000-44-44-44-440000000000000000000000000000000000000000000000000000
χ708-88-8-88-880000-44-444-44-40000000000000000000000000000000000000000000000000000
χ718-8-888-8-880000-444-4-444-40000000000000000000000000000000000000000000000000000
χ728-8-88-888-80000-444-44-4-440000000000000000000000000000000000000000000000000000

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