Finite Group Databasebeta

← Group #10858720

Character table — Group #10858720

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444888888888888888888888881212121212121616161616161616242424242424242424242448
order1222223444466644446688121212122244446666812121212121212122424242422448848121212122424444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11-11-1-1-1-1-1111-1-111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-11-11-1-1-1-1-1111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1111111-11-111111-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1111111-11-111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-11
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111111-1
χ911111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11-1-1-111-1-1-1-1-1-1-1-11111-11
χ1011111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1111111-1-1-1-11-1
χ1111111111111111-1-1-1-111111111-1-1-11-11-1-1-1-11-1-111-1-1111111111111-11-1-1-1-111-1-1-1-111-1-1111-1
χ1211111111111111-1-1-1-111111111-1-1-11-11-1-1-1-11-1-111-1-1111111-1-1-1-1-1-1-11-1-1-1-1111111-1-111-1-1-11
χ1311111111111111-1-1-1-111-1-11111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-11111-1-1-1-1
χ1411111111111111-1-1-1-111-1-11111111-11-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-1-11111
χ1511111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-11111111-11111-1-111-1-1-1-1-1-1-1-111
χ1611111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111111111-1-1
χ17222222-12222-1-1-12222-1-122-1-1-1-1222222-1-1-1-12-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-12222-1-122-1-1-1-1-2-22-22-211112-1-111-1-111-1-1-1-1000000-2-2-1-11111000000000000
χ19222222-12222-1-1-12222-1-1-2-2-1-1-1-122-22-22-1-1-1-1-2-1-1-1-1-1-1-1-11111000000-2-2111111000000000000
χ20222222-12222-1-1-12222-1-1-2-2-1-1-1-1-2-2-2-2-2-21111-2-1-111-1-11111110000002211-1-1-1-1000000000000
χ21222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-122-2-2-2-2-1-1-1-1211111111-1-1-1-10000002-211-1-111000000000000
χ22222222-12222-1-1-1-2-2-2-2-1-122-1-1-1-1-2-2-22-221111211-1-111-1-1-1-1-1-1000000-221111-1-1000000000000
χ23222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-1222-22-2-1-1-1-1-2111111111111000000-22-1-111-1-1000000000000
χ24222222-12222-1-1-1-2-2-2-2-1-1-2-2-1-1-1-1-2-222221111-211-1-111-1-111110000002-2-1-1-1-111000000000000
χ252222-2-222-22-222222-2-2-2-2222-2-2200-20200000-22200-2-20022-2-200000000-220000000000000000
χ262222-2-222-22-222222-2-2-2-2-2-22-2-220020-20000022200-2-200-2-222000000002-20000000000000000
χ272222-2-222-22-2222-2-222-2-2222-2-220020-200000-2-2-200220022-2-2000000002-20000000000000000
χ282222-2-222-22-2222-2-222-2-2-2-22-2-2200-202000002-2-2002200-2-22200000000-220000000000000000
χ292222-2-22-22-222220000-2-200-222-200020-200000002200-2-2000022-2-2-2-200000000000000000020
χ302222-2-22-22-222220000-2-200-222-200020-200000002200-2-20000-2-22222000000000000000000-20
χ312222-2-22-22-222220000-2-200-222-2000-2020000000-2-20022000022-2-222000000000000000000-20
χ322222-2-22-22-222220000-2-200-222-2000-2020000000-2-200220000-2-222-2-200000000000000000020
χ332222-2-2-12-22-2-1-1-122-2-21122-111-100-2020−i3−i3i3i3-2-1-1−i3i311−i3i3-1-111000000001-1−i3i3−i3i3000000000000
χ342222-2-2-12-22-2-1-1-122-2-21122-111-100-2020i3i3−i3−i3-2-1-1i3−i311i3−i3-1-111000000001-1i3−i3i3−i3000000000000
χ352222-2-2-12-22-2-1-1-122-2-211-2-2-111-10020-20−i3−i3i3i32-1-1−i3i311−i3i311-1-100000000-11i3−i3i3−i3000000000000
χ362222-2-2-12-22-2-1-1-122-2-211-2-2-111-10020-20i3i3−i3−i32-1-1i3−i311i3−i311-1-100000000-11−i3i3−i3i3000000000000
χ372222-2-2-12-22-2-1-1-1-2-2221122-111-10020-20−i3−i3i3i3-211i3−i3-1-1i3−i3-1-11100000000-11−i3i3i3−i3000000000000
χ382222-2-2-12-22-2-1-1-1-2-2221122-111-10020-20i3i3−i3−i3-211−i3i3-1-1−i3i3-1-11100000000-11i3−i3−i3i3000000000000
χ392222-2-2-12-22-2-1-1-1-2-22211-2-2-111-100-2020−i3−i3i3i3211i3−i3-1-1i3−i311-1-1000000001-1i3−i3−i3i3000000000000
χ402222-2-2-12-22-2-1-1-1-2-22211-2-2-111-100-2020i3i3−i3−i3211−i3i3-1-1−i3i311-1-1000000001-1−i3i3i3−i3000000000000
χ4122-2-22-2222-2-22-2-200002-20022-2-22-200002-22-200000000000002-22-200000000000000002-20000
χ4222-2-22-2222-2-22-2-200002-20022-2-22-200002-22-20000000000000-22-220000000000000000-220000
χ4322-2-22-2222-2-22-2-200002-20022-2-2-220000-22-2200000000000002-22-20000000000000000-220000
χ4422-2-22-2222-2-22-2-200002-20022-2-2-220000-22-220000000000000-22-2200000000000000002-20000
χ4522-2-22-22-2-2222-2-22i−2i2i−2i2-200-2-222000000000002i−2i002i−2i000000000000000000002i−2i0000002-200
χ4622-2-22-22-2-2222-2-22i−2i2i−2i2-200-2-222000000000002i−2i002i−2i00000000000000000000−2i2i000000-2200
χ4722-2-22-22-2-2222-2-2−2i2i−2i2i2-200-2-22200000000000−2i2i00−2i2i000000000000000000002i−2i000000-2200
χ4822-2-22-22-2-2222-2-2−2i2i−2i2i2-200-2-22200000000000−2i2i00−2i2i00000000000000000000−2i2i0000002-200
χ4922-2-2-222-222-22-2-22i−2i−2i2i-2200-22-22000000000002i−2i00−2i2i0000002-2-220000000000002i−2i00000000
χ5022-2-2-222-222-22-2-22i−2i−2i2i-2200-22-22000000000002i−2i00−2i2i000000-222-2000000000000−2i2i00000000
χ5122-2-2-222-222-22-2-2−2i2i2i−2i-2200-22-2200000000000−2i2i002i−2i0000002-2-22000000000000−2i2i00000000
χ5222-2-2-222-222-22-2-2−2i2i2i−2i-2200-22-2200000000000−2i2i002i−2i000000-222-20000000000002i−2i00000000
χ534444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-20022220000000000000−2i32i3002i3−2i3000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-20000-2-200222200000000000002i3−2i300−2i32i3000000000000000000000000000000
χ564444-4-4-2-44-44-2-2-2000022002-2-2200040-40000000-2-20022000000000000000000000000000000
χ574444-4-4-2-44-44-2-2-2000022002-2-22000-40400000002200-2-2000000000000000000000000000000
χ5844-4-44-4-244-4-4-2220000-2200-2-2224-40000-22-22000000000000000000000000000000000000000
χ5944-4-44-4-244-4-4-2220000-2200-2-222-4400002-22-2000000000000000000000000000000000000000
χ6044-4-44-4-2-4-444-2224i−4i4i−4i-220022-2-200000000000−2i2i00−2i2i00000000000000000000000000000000
χ6144-4-44-4-2-4-444-222−4i4i−4i4i-220022-2-2000000000002i−2i002i−2i00000000000000000000000000000000
χ6244-4-4-4444-4-444-4-40000-44004-44-40000000000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-44-22200002-200-22-22000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ6444-4-4-44-24-4-44-22200002-200-22-220000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ6544-4-4-44-2-444-4-2224i−4i−4i4i2-2002-22-200000000000−2i2i002i−2i00000000000000000000000000000000
χ6644-4-4-44-2-444-4-222−4i4i4i−4i2-2002-22-2000000000002i−2i00−2i2i00000000000000000000000000000000
χ674-44-40040000-44-4000000−2i22i200000000000000000000000−2i22i2000000−2i22i20000000000002-2000000
χ684-44-40040000-44-4000000−2i22i200000000000000000000000−2i22i20000002i2−2i2000000000000-22000000
χ694-44-40040000-44-40000002i2−2i2000000000000000000000002i2−2i2000000−2i22i2000000000000-22000000
χ704-44-40040000-44-40000002i2−2i2000000000000000000000002i2−2i20000002i2−2i20000000000002-2000000
χ718-88-800-400004-44000000−4i24i2000000000000000000000002i2−2i20000000000000000000000000000
χ728-88-800-400004-440000004i2−4i200000000000000000000000−2i22i20000000000000000000000000000
χ738-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-4000044-40000000000000000000000000000000002i6−2i600000000000000000000000000
χ758-8-8800-4000044-4000000000000000000000000000000000−2i62i600000000000000000000000000

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