Finite Group Databasebeta

← Group #10868081

Character table — Group #10868081

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666224444666612121212444448888121212121212121212122424242424242424444444412121212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-11111-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111-1-11111-1-1-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-111-1-11111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-111-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-111-1-11-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-111-1-111-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11-1-11111-1-1111-1-111-1
χ17222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-2000000000000000022-2-2-2-200000000020000000
χ18222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-20000000000000000-2-22222000000000-20000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000000002200000000000000002222-2-2000000000-20000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2-2-22200000000020000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-222-2-2-2-22211-1-1-1-11111-1-1-1-11111000000-2-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-222-2-211-1-1-1-111111111-1-1-1-1000000211-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2222222-2-2111111-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-222-2-222111111-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-22-2222-2-22-2-2-22-220022-2-200002-22-20000000000022-2-200000000000000000000000000002i−2i2i−2i000
χ30222-2-2-22-2222-2-22-2-2-22-220022-2-200002-22-20000000000022-2-20000000000000000000000000000−2i2i−2i2i000
χ31222-2-2-22-2222-2-22-2-2-22-2200-2-22200002-22-200000000000-2-22200000000000000000000000000002i−2i−2i2i000
χ32222-2-2-22-2222-2-22-2-2-22-2200-2-22200002-22-200000000000-2-2220000000000000000000000000000−2i2i2i−2i000
χ3322-22-2-2-222-22-22-222-22-2-2002i−2i2i−2i0000-2-22202i−2i00002-2002i−2i2i−2i000022-2-2000000000002i−2i00000000000000
χ3422-22-2-2-222-22-22-222-22-2-2002i−2i2i−2i0000-2-2220−2i2i0000-22002i−2i2i−2i0000-2-22200000000000−2i2i00000000000000
χ3522-22-2-2-222-22-22-222-22-2-200−2i2i−2i2i0000-2-22202i−2i0000-2200−2i2i−2i2i0000-2-222000000000002i−2i00000000000000
χ3622-22-2-2-222-22-22-222-22-2-200−2i2i−2i2i0000-2-2220−2i2i00002-200−2i2i−2i2i000022-2-200000000000−2i2i00000000000000
χ3722-22-2-2-22-1-22-221-1-11-111002i−2i2i−2i−i3−i3i3i311-1-102i−2i00002-2−i3i3−ii−ii33−3−3-1-111−i3−i3i3i30000000−ii3−3000000000000
χ3822-22-2-2-22-1-22-221-1-11-111002i−2i2i−2i−i3−i3i3i311-1-10−2i2i0000-22−i3i3−ii−ii33−3−311-1-1i3i3−i3−i30000000i−i−33000000000000
χ3922-22-2-2-22-1-22-221-1-11-111002i−2i2i−2ii3i3−i3−i311-1-102i−2i00002-2i3−i3−ii−ii−3−333-1-111i3i3−i3−i30000000−ii−33000000000000
χ4022-22-2-2-22-1-22-221-1-11-111002i−2i2i−2ii3i3−i3−i311-1-10−2i2i0000-22i3−i3−ii−ii−3−33311-1-1−i3−i3i3i30000000i−i3−3000000000000
χ4122-22-2-2-22-1-22-221-1-11-11100−2i2i−2i2i−i3−i3i3i311-1-102i−2i0000-22−i3i3i−ii−i−3−33311-1-1i3i3−i3−i30000000−ii3−3000000000000
χ4222-22-2-2-22-1-22-221-1-11-11100−2i2i−2i2i−i3−i3i3i311-1-10−2i2i00002-2−i3i3i−ii−i−3−333-1-111−i3−i3i3i30000000i−i−33000000000000
χ4322-22-2-2-22-1-22-221-1-11-11100−2i2i−2i2ii3i3−i3−i311-1-102i−2i0000-22i3−i3i−ii−i33−3−311-1-1−i3−i3i3i30000000−ii−33000000000000
χ4422-22-2-2-22-1-22-221-1-11-11100−2i2i−2i2ii3i3−i3−i311-1-10−2i2i00002-2i3−i3i−ii−i33−3−3-1-111i3i3−i3−i30000000i−i3−3000000000000
χ4522-2-222-2-222-2-22-2-2-2222-200000000002-2-220002i−2i00000000002i−2i2i−2i000000002i−2i002i−2i00000002-200000000
χ4622-2-222-2-222-2-22-2-2-2222-200000000002-2-220002i−2i00000000002i−2i2i−2i00000000−2i2i00−2i2i0000000-2200000000
χ4722-2-222-2-222-2-22-2-2-2222-200000000002-2-22000−2i2i0000000000−2i2i−2i2i000000002i−2i002i−2i0000000-2200000000
χ4822-2-222-2-222-2-22-2-2-2222-200000000002-2-22000−2i2i0000000000−2i2i−2i2i00000000−2i2i00−2i2i00000002-200000000
χ4922-2-222-2-22-222-2-2-2-2222-2002i−2i−2i2i0000-222-2000000000002i−2i−2i2i0000000000002i−2i00−2i2i000002-20000000000
χ5022-2-222-2-22-222-2-2-2-2222-2002i−2i−2i2i0000-222-2000000000002i−2i−2i2i000000000000−2i2i002i−2i00000-220000000000
χ5122-2-222-2-22-222-2-2-2-2222-200−2i2i2i−2i0000-222-200000000000−2i2i2i−2i0000000000002i−2i00−2i2i00000-220000000000
χ5222-2-222-2-22-222-2-2-2-2222-200−2i2i2i−2i0000-222-200000000000−2i2i2i−2i000000000000−2i2i002i−2i000002-20000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-22222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-4-44-44-4-4444-4-4-44-440000000000-44-4400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-244-4-4-2222-22-20044-4-40000-22-2200000000000-2-22200000000000000000000000000000000000
χ57444-4-4-44-4-244-4-4-2222-22-200-4-4440000-22-220000000000022-2-200000000000000000000000000000000000
χ58444-4-4-44-4-2-4-444-2222-22-200000000002-22-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ59444-4-4-44-4-2-4-444-2222-22-200000000002-22-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6044-44-4-4-4444-44-4-444-44-4-4000000000044-4-400000000000000000000000000000000000000000000000000
χ6144-44-4-4-44-24-44-42-2-22-222000000−2i3−2i32i32i3-2-2220000000002i3−2i3000000000000000000000000000000000000000
χ6244-44-4-4-44-24-44-42-2-22-2220000002i32i3−2i3−2i3-2-222000000000−2i32i3000000000000000000000000000000000000000
χ6344-4-444-4-4-24-4-44222-2-2-220000000000-222-20004i−4i0000000000−2i2i−2i2i0000000000000000000000000000000
χ6444-4-444-4-4-24-4-44222-2-2-220000000000-222-2000−4i4i00000000002i−2i2i−2i0000000000000000000000000000000
χ6544-4-444-4-4-2-444-4222-2-2-22004i−4i−4i4i00002-2-2200000000000−2i2i2i−2i00000000000000000000000000000000000
χ6644-4-444-4-4-2-444-4222-2-2-2200−4i4i4i−4i00002-2-22000000000002i−2i−2i2i00000000000000000000000000000000000
χ674-4444-4-4-44000044-44-4-4-4000000000000000000022−22000000000000000022−2222−2200000000000000000000000
χ684-4444-4-4-44000044-44-4-4-40000000000000000000−22220000000000000000−2222−222200000000000000000000000
χ694-4444-4-4-4-20000-2-22-2222000000−2i32i3−2i32i300000000022−22000000000000i6−i6i6−i6−22−2200000000000000000000000
χ704-4444-4-4-4-20000-2-22-2222000000−2i32i3−2i32i3000000000−2222000000000000−i6i6−i6i62−22−200000000000000000000000
χ714-4444-4-4-4-20000-2-22-22220000002i3−2i32i3−2i300000000022−22000000000000−i6i6−i6i6−22−2200000000000000000000000
χ724-4444-4-4-4-20000-2-22-22220000002i3−2i32i3−2i3000000000−2222000000000000i6−i6i6−i62−22−200000000000000000000000
χ734-44-4-44-44400004-44-4-44-400000000000000000000000000000000000000000004i−4i0000000000000000000
χ744-44-4-44-44400004-44-4-44-40000000000000000000000000000000000000000000−4i4i0000000000000000000
χ754-4-44-444-440000-44-4-4-4444-400004-4-44000000000000000000000000000000000000000000000000000000
χ764-4-44-444-440000-44-4-4-444-440000-444-4000000000000000000000000000000000000000000000000000000
χ774-4-44-444-4-200002-2222-2-24-40000-222-200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ784-4-44-444-4-200002-2222-2-24-40000-222-200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ794-4-44-444-4-200002-2222-2-2-4400002-2-2200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ804-4-44-444-4-200002-2222-2-2-4400002-2-2200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ814-4-4-44-44440000-4-444-4-44000000000000000000000000000000000000000000000000000000000000022−220
χ824-4-4-44-44440000-4-444-4-440000000000000000000000000000000000000000000000000000000000000−22220
χ838-88-8-88-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-88-888-4000044-4-444-40000000000000000000000000000000000000000000000000000000000000000

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