Finite Group Databasebeta

← Group #10695780

Character table — Group #10695780

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222244444444888888888888888816161616161616161616161624242424242424242424242424242424
order12222222222236666666444466664444121212121212121212121212444412121212121212124444444488888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111-1-1-1-111111111-1-1-1-1
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
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211111111-1-1-1-12-22-2-1-111-1-1110000000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211111111-1-1-1-1-22-2211-1-111-1-10000000000000000
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−i3i3i3−i3−i3i3i3−i30000000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2221111-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-200000000000022-2-2020-2002200-2-20000000000000000
χ2022222222-2-2-2-2222222222-22-2-2-2-2-200000000000022-2-20-20200-2-200220000000000000000
χ2122222222-2-2-2-222222222-22-22-2-2-2-2000000000000-2-22220-202200-2-2000000000000000000
χ2222222222-2-2-2-222222222-22-22-2-2-2-2000000000000-2-222-2020-2-20022000000000000000000
χ2322222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3−i3−i3i3i3-1-111020-2−i3i3-1-1i3−i3110000000000000000
χ2422222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000−i3−i3i3i3−i3−i3i3i3-1-1110-202i3−i311−i3i3-1-10000000000000000
χ2522222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3i3i3−i3−i3-1-111020-2i3−i3-1-1−i3i3110000000000000000
χ2622222222-2-2-2-2-1-1-1-1-1-1-1-12-22-211110000i3i3−i3−i3i3i3−i3−i3-1-1110-202−i3i311i3−i3-1-10000000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-120-20-1-1−i3i311i3−i30000000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-1-202011i3−i3-1-1−i3i30000000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-120-20-1-1i3−i311−i3i30000000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-1-202011−i3i3-1-1i3−i30000000000000000
χ3122-22-2-2-222-2-22222-22-2-2-2000022-2-2002-200002-22-2000000000000000000000000−i2−i2i2i2−i2−i2i2i2
χ3222-22-2-2-222-2-22222-22-2-2-2000022-2-2002-200002-22-2000000000000000000000000i2i2−i2−i2i2i2−i2−i2
χ3322-22-2-2-222-2-22222-22-2-2-2000022-2-200-220000-22-22000000000000000000000000−i2−i2i2i2i2i2−i2−i2
χ3422-22-2-2-222-2-22222-22-2-2-2000022-2-200-220000-22-22000000000000000000000000i2i2−i2−i2−i2−i2i2i2
χ352-22-22-2-22-22-2222-22-22-2-200002-22-22-2002-22-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ362-22-22-2-22-22-2222-22-22-2-200002-22-22-2002-22-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ372-22-22-2-22-22-2222-22-22-2-200002-22-2-2200-22-220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ382-22-22-2-22-22-2222-22-22-2-200002-22-2-2200-22-220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ392-2-2-2-222222-2-222-2-2-2-22222-2-2-222-20000000000002-22-200000000000000002i2i−2i−2i00000000
χ402-2-2-2-222222-2-222-2-2-2-22222-2-2-222-20000000000002-22-20000000000000000−2i−2i2i2i00000000
χ412-2-2-2-222222-2-222-2-2-2-222-2-222-222-2000000000000-22-2200000000000022-2-2000000000000
χ422-2-2-2-222222-2-222-2-2-2-222-2-222-222-2000000000000-22-22000000000000-2-222000000000000
χ432-2-2-2-2222-2-22222-2-2-2-2222-2-222-2-220000000000002-2-22000000000000000000002-2-220000
χ442-2-2-2-2222-2-22222-2-2-2-2222-2-222-2-220000000000002-2-2200000000000000000000-222-20000
χ452-2-2-2-2222-2-22222-2-2-2-222-222-22-2-22000000000000-222-20000000000000000000000002-2-22
χ462-2-2-2-2222-2-22222-2-2-2-222-222-22-2-22000000000000-222-2000000000000000000000000-222-2
χ47444-4-44-4-400004-444-4-44-400000000000000000000000000000000000000002-22-200000000
χ48444-4-44-4-400004-444-4-44-40000000000000000000000000000000000000000-22-2200000000
χ4944-44-4-4-444-4-44-2-2-22-22220000-2-222004-40000-22-2200000000000000000000000000000000
χ5044-44-4-4-444-4-44-2-2-22-22220000-2-22200-4400002-22-200000000000000000000000000000000
χ5144-44-4-4-44-444-4444-44-4-4-40000-4-44400000000000000000000000000000000000000000000
χ5244-44-4-4-44-444-4-2-2-22-2222000022-2-200000000−2i32i32i3−2i300000000000000000000000000000000
χ5344-44-4-4-44-444-4-2-2-22-2222000022-2-2000000002i3−2i3−2i32i300000000000000000000000000000000
χ5444-4-44-44-400004-44-4-44-440000000000000000000000000000000000002i−2i2i−2i000000000000
χ5544-4-44-44-400004-44-4-44-44000000000000000000000000000000000000−2i2i−2i2i000000000000
χ564-444-4-44-400004-4-444-4-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ574-444-4-44-400004-4-444-4-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ584-44-44-4-444-44-444-44-44-4-40000-44-4400000000000000000000000000000000000000000000
χ594-44-44-4-444-44-4-2-22-22-22200002-22-20000−2i32i32i3−2i3000000000000000000000000000000000000
χ604-44-44-4-444-44-4-2-22-22-22200002-22-200002i3−2i3−2i32i3000000000000000000000000000000000000
χ614-44-44-4-44-44-44-2-22-22-2220000-22-224-400-22-22000000000000000000000000000000000000
χ624-44-44-4-44-44-44-2-22-22-2220000-22-22-44002-22-2000000000000000000000000000000000000
χ634-4-4444-4-400004-4-4-4444-400000000000000000000000000000000000000002i−2i−2i2i00000000
χ644-4-4444-4-400004-4-4-4444-40000000000000000000000000000000000000000−2i2i2i−2i00000000
χ654-4-4-4-444444-4-4-2-22222-2-244-4-42-2-22000000000000-22-220000000000000000000000000000
χ664-4-4-4-444444-4-4-2-22222-2-2-4-4442-2-220000000000002-22-20000000000000000000000000000
χ674-4-4-4-4444-4-444-2-22222-2-24-4-44-222-2000000000000-222-20000000000000000000000000000
χ684-4-4-4-4444-4-444-2-22222-2-2-444-4-222-20000000000002-2-220000000000000000000000000000
χ69888-8-88-8-80000-44-4-444-440000000000000000000000000000000000000000000000000000
χ7088-8-88-88-80000-44-444-44-40000000000000000000000000000000000000000000000000000
χ718-888-8-88-80000-444-4-444-40000000000000000000000000000000000000000000000000000
χ728-8-8888-8-80000-4444-4-4-440000000000000000000000000000000000000000000000000000

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