Finite Group Databasebeta

← Group #10778232

Character table — Group #10778232

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order122234444444466612121212244444466121212121212246688881212121212121212242424242424242488884412121212888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ911111-1-1-1-11111111-1-1-1-1-111111-1-1-1111-1-11-1-1-1-111-1-1111-111-1-11111-1-1-1-111-1-11-111-1-111-1-11-111-1-11-1
χ1011111-1-1-1-11111111-1-1-1-1-111111-1-1-1111-1-11-1-1-1-111-1-1111-111-1-11111-1-1-1-1-1-1111-111-1-1-1-111-11-1-111-11
χ1111111-1-1-1-11111111-1-1-1-1-111111-1-1-1111-1-11-1-1-1-1-1-111111-111-1-1-1-1-1-1111111-1-1-11-1-111-1-1111-111-1-1-11
χ1211111-1-1-1-11111111-1-1-1-1-111111-1-1-1111-1-11-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-111-11-1-11111-1-1-11-1-1111-1
χ1311111-1-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1111-1-11111111-1-1-1-11-1-1-1111111-1-1-1-111-1-1-11-1-11111-1-11-1-1-111-11
χ1411111-1-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1111-1-11111111-1-1-1-11-1-1-1111111-1-1-1-1-1-111-11-1-111-1-111-1111-1-11-1
χ1511111-1-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1111-1-111111-1-111-1-11-1-1-111-1-1-1-1111111-1-11-111-1-1-1-1111-1-1-1111-1
χ1611111-1-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1111-1-111111-1-111-1-11-1-1-111-1-1-1-11111-1-1111-111-1-111-1-1-1111-1-1-11
χ17222222222-2-2222222222-2-20000-2-2-2-22222-20000000000-2-200000000000022220000000000-2-2000000
χ18222222222-2-2222222222-2-20000-2-2-2-22222-20000000000-2-2000000000000-2-2-2-2000000000022000000
χ192222222-2-222-2-2222-2-2-2-2-2-222-2-22-2-22-2-22222-2220000-2-2-2222-2-2000000000000000000000000000000
χ202222222-2-222-2-2222-2-2-2-2-2-2-2-2222-2-22-2-2222-22-2-2000022-22-2-222000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2220000-222-2-2-222-200000000002-200000000000000000000000000002i−2i2i−2i00
χ222222222-2-2-2-2-2-2222-2-2-2-2220000-222-2-2-222-200000000002-20000000000000000000000000000−2i2i−2i2i00
χ2322222-2-22222-2-222222222-222-2-2-2222-2-2-2-22-22-2-20000-2-2-2-22222000000000000000000000000000000
χ2422222-2-22222-2-222222222-2-2-222-2222-2-2-2-222-222000022-2-2-2-2-2-2000000000000000000000000000000
χ2522222-2-222-2-2-2-22222222-2200002-2-2-2-2-2-2-2-200000000002200000000000000000000000000002i−2i−2i2i00
χ2622222-2-222-2-2-2-22222222-2200002-2-2-2-2-2-2-2-20000000000220000000000000000000000000000−2i2i2i−2i00
χ2722222-2-2-2-2-2-222222-2-2-2-22-20000222-222-2-2-20000000000-2200000000000022-2-20000000000-22000000
χ2822222-2-2-2-2-2-222222-2-2-2-22-20000222-222-2-2-20000000000-22000000000000-2-22200000000002-2000000
χ292222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-211222211-1-11111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-122-2-2-2-22-1-1-1-1-1-1-1-1-2-211-2-2-2-211-1-1111111111111000022-1-1-1-1000000000000
χ332222-122-2-222-2-2-1-1-11111-2-222-2-2211-111-1-1-12-2-1-10000111-1-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ342222-122-2-222-2-2-1-1-11111-2-222-2-2211-111-1-1-12-2-1-10000111-1-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ352222-122-2-222-2-2-1-1-11111-2-2-2-222211-111-1-1-1-22110000-1-11-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ362222-122-2-222-2-2-1-1-11111-2-2-2-222211-111-1-1-1-22110000-1-11-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ372222-1-2-22222-2-2-1-1-1-1-1-1-12-222-2-2-2-1-1-11111-1-221100001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ382222-1-2-22222-2-2-1-1-1-1-1-1-12-222-2-2-2-1-1-11111-1-221100001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ392222-1-2-22222-2-2-1-1-1-1-1-1-12-2-2-222-2-1-1-11111-12-2-1-10000-1-1111111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ402222-1-2-22222-2-2-1-1-1-1-1-1-12-2-2-222-2-1-1-11111-12-2-1-10000-1-1111111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ412222-1-2-2-2-22222-1-1-11111-222222-211-1-1-111-1-2-21122-2-2-1-1-11-1-111-1-1-1-1111100002-2-1-111000000000000
χ422222-1-2-2-2-22222-1-1-11111-222222-211-1-1-111-1-2-211-2-222-1-1-11-1-1111111-1-1-1-10000-2211-1-1000000000000
χ432222-1-2-2-2-22222-1-1-11111-22-2-2-2-2-211-1-1-111-122-1-122-2-211-1111-1-1-1-1-1-111110000-2211-1-1000000000000
χ442222-1-2-2-2-22222-1-1-11111-22-2-2-2-2-211-1-1-111-122-1-1-2-22211-1111-1-11111-1-1-1-100002-2-1-111000000000000
χ452-2-2222i−2i2i−2i002-2-22-22i2i−2i−2i00000000002-22i−2i000002−2−i2i2000000002−22−2−i2i2−i2i22-22i−2i0000002−2−i2i200000000
χ462-2-2222i−2i2i−2i002-2-22-22i2i−2i−2i00000000002-22i−2i000002−2−i2i2000000002−22−2−i2i2−i2i2-22−2i2i000000−22i2−i200000000
χ472-2-2222i−2i2i−2i002-2-22-22i2i−2i−2i00000000002-22i−2i00000−22i2−i200000000−22−22i2−i2i2−i22-22i−2i000000−22i2−i200000000
χ482-2-2222i−2i2i−2i002-2-22-22i2i−2i−2i00000000002-22i−2i00000−22i2−i200000000−22−22i2−i2i2−i2-22−2i2i0000002−2−i2i200000000
χ492-2-222−2i2i−2i2i002-2-22-2−2i−2i2i2i00000000002-2−2i2i000002−2i2−i2000000002−22−2i2−i2i2−i22-2−2i2i0000002−2i2−i200000000
χ502-2-222−2i2i−2i2i002-2-22-2−2i−2i2i2i00000000002-2−2i2i000002−2i2−i2000000002−22−2i2−i2i2−i2-222i−2i000000−22−i2i200000000
χ512-2-222−2i2i−2i2i002-2-22-2−2i−2i2i2i00000000002-2−2i2i00000−22−i2i200000000−22−22−i2i2−i2i22-2−2i2i000000−22−i2i200000000
χ522-2-222−2i2i−2i2i002-2-22-2−2i−2i2i2i00000000002-2−2i2i00000−22−i2i200000000−22−22−i2i2−i2i2-222i−2i0000002−2i2−i200000000
χ534444-24444-4-444-2-2-2-2-2-2-2-4-40000-4222-2-2-2-220000000000220000000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-22222440000-4-2-2222-2-220000000000-220000000000000000000000000000000000
χ554444-2-4-444-4-4-4-4-2-2-2-2-2-2-2-4400004222222220000000000-2-20000000000000000000000000000000000
χ564444-2-4-4-4-4-4-444-2-2-222224-400004-2-22-2-222200000000002-20000000000000000000000000000000000
χ574-44-4400004-4004-4-4000000004-400040000-4000000004-4000000000000000000000000000000000000
χ584-44-4400004-4004-4-400000000-4400040000-400000000-44000000000000000000000000000000000000
χ594-44-440000-44004-4-40000004i−4i00000-4000040000000000004i−4i00000000000000000000000000000000
χ604-44-440000-44004-4-4000000−4i4i00000-400004000000000000−4i4i00000000000000000000000000000000
χ614-44-4-200004-400-222−2i32i3−2i32i300004-40−2i32i3-20000200−2i32i30000-22000000000000000000000000000000000000
χ624-44-4-200004-400-222−2i32i3−2i32i30000-440−2i32i3-200002002i3−2i300002-2000000000000000000000000000000000000
χ634-44-4-200004-400-2222i3−2i32i3−2i300004-402i3−2i3-200002002i3−2i30000-22000000000000000000000000000000000000
χ644-44-4-200004-400-2222i3−2i32i3−2i30000-4402i3−2i3-20000200−2i32i300002-2000000000000000000000000000000000000
χ654-44-4-20000-4400-222−2i32i3−2i32i3004i−4i0002i3−2i320000-2000000000000−2i2i23−23000000000000000000000000000000
χ664-44-4-20000-4400-222−2i32i3−2i32i300−4i4i0002i3−2i320000-20000000000002i−2i−2323000000000000000000000000000000
χ674-44-4-20000-4400-2222i3−2i32i3−2i3004i−4i000−2i32i320000-2000000000000−2i2i−2323000000000000000000000000000000
χ684-44-4-20000-4400-2222i3−2i32i3−2i300−4i4i000−2i32i320000-20000000000002i−2i23−23000000000000000000000000000000
χ694-4-4444i−4i−4i4i00-44-44-4−4i−4i4i4i0000000000-444i−4i00000000000000000000000000000000000000000000000
χ704-4-444−4i4i4i−4i00-44-44-44i4i−4i−4i0000000000-44−4i4i00000000000000000000000000000000000000000000000
χ714-4-44-24i−4i4i−4i004-42-22−2i−2i2i2i0000000000-22−2i2i0000022−22−2i22i200000000−22−22i2−i2i2−i20000000000000000000000
χ724-4-44-24i−4i4i−4i004-42-22−2i−2i2i2i0000000000-22−2i2i00000−22222i2−2i2000000002−22−2−i2i2−i2i20000000000000000000000
χ734-4-44-24i−4i−4i4i00-442-222i2i−2i−2i00000000002-2−2i2i00000000000000000i6−i6−i6i66−6−660000000000000000000000
χ744-4-44-24i−4i−4i4i00-442-222i2i−2i−2i00000000002-2−2i2i00000000000000000−i6i6i6−i6−666−60000000000000000000000
χ754-4-44-2−4i4i4i−4i00-442-22−2i−2i2i2i00000000002-22i−2i00000000000000000i6−i6−i6i6−666−60000000000000000000000
χ764-4-44-2−4i4i4i−4i00-442-22−2i−2i2i2i00000000002-22i−2i00000000000000000−i6i6i6−i66−6−660000000000000000000000
χ774-4-44-2−4i4i−4i4i004-42-222i2i−2i−2i0000000000-222i−2i0000022−222i2−2i200000000−22−22−i2i2−i2i20000000000000000000000
χ784-4-44-2−4i4i−4i4i004-42-222i2i−2i−2i0000000000-222i−2i00000−2222−2i22i2000000002−22−2i2−i2i2−i20000000000000000000000
χ7988-8-8800000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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