Finite Group Databasebeta

← Group #10698518

Character table — Group #10698518

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222244444444888888888888888816161616161616161616161624242424242424242424242424242424
order122222222222366666664444666644441212121212121212121212122444661212121212124444444488888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
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
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211111111-1-1-1-122-2-2-1-1-1-111110000000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211111111-1-1-1-1-2-2221111-1-1-1-10000000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2221111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2221111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-200000000000022-2-2002-2000022-2-20000000000000000
χ2022222222-2-2-2-2222222222-22-2-2-2-2-200000000000022-2-200-220000-2-2220000000000000000
χ2122222222-2-2-2-222222222-22-22-2-2-2-2000000000000-2-2222-20022-2-200000000000000000000
χ2222222222-2-2-2-222222222-22-22-2-2-2-2000000000000-2-222-2200-2-22200000000000000000000
χ2322222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3−i3−i3i3i3-1-111002-2−i3i3i3−i3-1-1110000000000000000
χ2422222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3−i3−i3i3i3-1-11100-22i3−i3−i3i311-1-10000000000000000
χ2522222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3i3i3−i3−i3-1-111002-2i3−i3−i3i3-1-1110000000000000000
χ2622222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3i3i3−i3−i3-1-11100-22−i3i3i3−i311-1-10000000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-12-200-1-111−i3i3i3−i30000000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-1-220011-1-1i3−i3−i3i30000000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-12-200-1-111i3−i3−i3i30000000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-1-220011-1-1−i3i3i3−i30000000000000000
χ312222-2-2-2-22-2-2222-222-2-2-2000022-2-2002i−2i00002i−2i2i−2i000000000000000000000000−i2−i2i2i222−2−2
χ322222-2-2-2-22-2-2222-222-2-2-2000022-2-2002i−2i00002i−2i2i−2i000000000000000000000000i2i2−i2−i2−2−222
χ332222-2-2-2-22-2-2222-222-2-2-2000022-2-200−2i2i0000−2i2i−2i2i000000000000000000000000−i2−i2i2i2−2−222
χ342222-2-2-2-22-2-2222-222-2-2-2000022-2-200−2i2i0000−2i2i−2i2i000000000000000000000000i2i2−i2−i222−2−2
χ352-22-22-22-222-2-22-2-22-22-222-2-222-22-20000000000002-22-20000000000000000000000002i−2i2i−2i
χ362-22-22-22-222-2-22-2-22-22-222-2-222-22-20000000000002-22-2000000000000000000000000−2i2i−2i2i
χ372-22-22-22-222-2-22-2-22-22-22-222-22-22-2000000000000-22-22000000000000000000002i−2i2i−2i0000
χ382-22-22-22-222-2-22-2-22-22-22-222-22-22-2000000000000-22-2200000000000000000000−2i2i−2i2i0000
χ392-22-22-22-2-2-2222-2-22-22-2222-2-2-22-220000000000002-2-220000000000002i2i−2i−2i000000000000
χ402-22-22-22-2-2-2222-2-22-22-2222-2-2-22-220000000000002-2-22000000000000−2i−2i2i2i000000000000
χ412-22-22-22-2-2-2222-2-22-22-22-2-222-22-22000000000000-222-2000000000000000022-2-200000000
χ422-22-22-22-2-2-2222-2-22-22-22-2-222-22-22000000000000-222-20000000000000000-2-22200000000
χ432-22-2-22-222-22-22-222-2-22-200002-2-222i−2i002i−2i2i−2i00000000000000000000000000002−2−22−i2i2i2−i2
χ442-22-2-22-222-22-22-222-2-22-200002-2-222i−2i002i−2i2i−2i0000000000000000000000000000−222−2i2−i2−i2i2
χ452-22-2-22-222-22-22-222-2-22-200002-2-22−2i2i00−2i2i−2i2i00000000000000000000000000002−2−22i2−i2−i2i2
χ462-22-2-22-222-22-22-222-2-22-200002-2-22−2i2i00−2i2i−2i2i0000000000000000000000000000−222−2−i2i2i2−i2
χ474444-4-4-4-44-4-44-2-22-2-22220000-2-222004i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ484444-4-4-4-44-4-44-2-22-2-22220000-2-22200−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ494444-4-4-4-4-444-444-444-4-4-40000-4-44400000000000000000000000000000000000000000000
χ504444-4-4-4-4-444-4-2-22-2-2222000022-2-20000000023−23−232300000000000000000000000000000000
χ514444-4-4-4-4-444-4-2-22-2-2222000022-2-200000000−232323−2300000000000000000000000000000000
χ5244-4-44-4-440000444-4-44-4-400000000000000000000000000000000000000002i−2i2i−2i00000000
χ5344-4-44-4-440000444-4-44-4-40000000000000000000000000000000000000000−2i2i−2i2i00000000
χ5444-4-4-444-4000044-4-4-4-4440000000000000000000000000000000000002i−2i2i−2i000000000000
χ5544-4-4-444-4000044-4-4-4-444000000000000000000000000000000000000−2i2i−2i2i000000000000
χ564-44-44-44-444-4-4-222-22-22-24-4-44-22-22000000000000-22-220000000000000000000000000000
χ574-44-44-44-444-4-4-222-22-22-2-444-4-22-220000000000002-22-20000000000000000000000000000
χ584-44-44-44-4-4-444-222-22-22-244-4-42-22-2000000000000-222-20000000000000000000000000000
χ594-44-44-44-4-4-444-222-22-22-2-4-4442-22-20000000000002-2-220000000000000000000000000000
χ604-44-4-44-444-44-4-22-2-222-220000-222-24i−4i00−2i2i−2i2i000000000000000000000000000000000000
χ614-44-4-44-444-44-4-22-2-222-220000-222-2−4i4i002i−2i2i−2i000000000000000000000000000000000000
χ624-44-4-44-44-44-444-444-4-44-40000-444-400000000000000000000000000000000000000000000
χ634-44-4-44-44-44-44-22-2-222-2200002-2-22000023−23−2323000000000000000000000000000000000000
χ644-44-4-44-44-44-44-22-2-222-2200002-2-220000−232323−23000000000000000000000000000000000000
χ654-4-4444-4-400004-4-4-4444-400000000000000000000000000000000000000002i−2i−2i2i00000000
χ664-4-4444-4-400004-4-4-4444-40000000000000000000000000000000000000000−2i2i2i−2i00000000
χ674-4-44-4-44400004-44-44-4-440000000000000000000000000000000000002-2-22000000000000
χ684-4-44-4-44400004-44-44-4-44000000000000000000000000000000000000-222-2000000000000
χ6988-8-88-8-880000-4-4-444-4440000000000000000000000000000000000000000000000000000
χ7088-8-8-888-80000-4-44444-4-40000000000000000000000000000000000000000000000000000
χ718-8-8888-8-80000-4444-4-4-440000000000000000000000000000000000000000000000000000
χ728-8-88-8-8880000-44-44-444-40000000000000000000000000000000000000000000000000000

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