Finite Group Databasebeta

← Group #10846003

Character table — Group #10846003

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212224444446666121212121212121212121212121288888888246612124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-111111111111-1-1-1-1-1-111111-111-1-11-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1-1-11111-1-11-1
χ10111111111-1-1-1-111111111111-1-1-1-1-1-111111-111-1-11-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-111-1-111-1-1-1-111-11
χ11111111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1111-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-11-1-11111-1-111-1-1-11
χ12111111111-1-1-1-111111111111-1-1-1-1-1-111111-1-1-1111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-1-111-1-1111-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1111-1-1-11-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-111-1-111-11
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1111-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-111-1-11-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-11-1-111-11-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-111-1-1-1-1111-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-11-1-111-11-1-111-1-1-1-1-1-11111-1-111-1-1-1-111111-111-1-1-1-11111-1-1-11
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-22-20000-2222-2-2-2-200000000-2-222000000000000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-2-2200002-2-2-222-2-20000000022-2-2000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2220000-2-222222200000000-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000022-2-2-2-222000000002222000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-111111111-1-1-1-100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-1-1-1111100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-111112-20000-22-1-11111−i3−i3i3i3−i3−i3i3i311-1-10000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-111112-20000-22-1-11111i3i3−i3−i3i3i3−i3−i311-1-10000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2200002-211-1-111−i3−i3i3i3−i3−i3i3i3-1-1110000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2200002-211-1-111i3i3−i3−i3i3i3−i3−i3-1-1110000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-12-222-2-22-2-1-11111-1-1-1-11111-1-111000000002-2-1-1110000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-12-2-2-2222-2-1-111111111-1-1-1-1-1-11100000000-2211-1-10000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2222-2-2-2211-1-111-1-1-1-1111111-1-100000000-2211-1-10000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1-22-2-222-2211-1-1111111-1-1-1-111-1-1000000002-2-1-1110000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111220000-2-2-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i311110000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111220000-2-2-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i311110000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-2-20000221111-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-10000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-2-20000221111-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-10000000000−i3i3i3−i30000000000
χ3722-22-2-2-22200002-22-22-2-2-22-2200000022-2-2002-200000000002-22-20000000000002i2i−2i−2i0000002i−2i00000000
χ3822-22-2-2-22200002-22-22-2-2-22-2200000022-2-2002-200000000002-22-2000000000000−2i−2i2i2i000000−2i2i00000000
χ3922-22-2-2-22200002-22-22-2-2-22-2200000022-2-200-220000000000-22-220000000000002i2i−2i−2i000000−2i2i00000000
χ4022-22-2-2-22200002-22-22-2-2-22-2200000022-2-200-220000000000-22-22000000000000−2i−2i2i2i0000002i−2i00000000
χ412-22-2-22-22222-2-222-2-2-2-222-2-222-222-2-22-22-20000000000002-20000000000002i2i−2i−2i2i−2i2i−2i0000000000000000
χ422-22-2-22-22222-2-222-2-2-2-222-2-222-222-2-22-22-20000000000002-2000000000000−2i−2i2i2i−2i2i−2i2i0000000000000000
χ432-22-2-22-22222-2-2-2-222-2-222-2-22-2222-2-2-22-22000000000000-220000000000000000000000000000002-22-200
χ442-22-2-22-22222-2-2-2-222-2-222-2-22-2222-2-2-22-22000000000000-22000000000000000000000000000000-22-2200
χ452-22-2-22-222-2-22222-2-2-2-222-2-22-22-2-2222-22-2000000000000-220000000000002i2i−2i−2i−2i2i−2i2i0000000000000000
χ462-22-2-22-222-2-22222-2-2-2-222-2-22-22-2-2222-22-2000000000000-22000000000000−2i−2i2i2i2i−2i2i−2i0000000000000000
χ472-22-2-22-222-2-222-2-222-2-222-2-222-2-2-222-22-220000000000002-20000000000000000000000000000002-2-2200
χ482-22-2-22-222-2-222-2-222-2-222-2-222-2-2-222-22-220000000000002-2000000000000000000000000000000-222-200
χ492-2-2-22-222200002-2-22-22-2-2-2220000002-2-2200002-20000000000002-22-2000000002-2-22000000002-2000000
χ502-2-2-22-222200002-2-22-22-2-2-2220000002-2-2200002-20000000000002-22-200000000-222-200000000-22000000
χ512-2-2-22-222200002-2-22-22-2-2-2220000002-2-220000-22000000000000-22-22000000002-2-2200000000-22000000
χ522-2-2-22-222200002-2-22-22-2-2-2220000002-2-220000-22000000000000-22-2200000000-222-2000000002-2000000
χ53444-44-4-4-4400000000444-4-4-4-400000000000000000000000000000000000022−2222−2200000000000000000000
χ54444-44-4-4-4400000000444-4-4-4-4000000000000000000000000000000000000−2222−222200000000000000000000
χ5544-44-4-4-4440000-44-444-4-4-44-44000000-4-44400000000000000000000000000000000000000000000000000
χ5644-44-4-4-44-200004-44-4-2222-22-2000000-2-222004-40000000000-22-2200000000000000000000000000000000
χ5744-44-4-4-44-200004-44-4-2222-22-2000000-2-22200-4400000000002-22-200000000000000000000000000000000
χ5844-44-4-4-44-20000-44-44-2222-22-200000022-2-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ5944-44-4-4-44-20000-44-44-2222-22-200000022-2-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ6044-4-4-444-444i−4i4i−4i00004-4-44-44-4004i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ6144-4-4-444-44−4i4i−4i4i00004-4-44-44-400−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ6244-4-4-444-4-24i−4i4i−4i0000-222-22-2200−2i2i−2i2i00000000000000−2i32i3000000000023−2300000000000000000000000000
χ6344-4-4-444-4-24i−4i4i−4i0000-222-22-2200−2i2i−2i2i000000000000002i3−2i30000000000−232300000000000000000000000000
χ6444-4-4-444-4-2−4i4i−4i4i0000-222-22-22002i−2i2i−2i00000000000000−2i32i30000000000−232300000000000000000000000000
χ6544-4-4-444-4-2−4i4i−4i4i0000-222-22-22002i−2i2i−2i000000000000002i3−2i3000000000023−2300000000000000000000000000
χ664-444-4-44-4400000000-4-44-444-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ674-444-4-44-4400000000-4-44-444-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ684-44-4-44-44-244-4-444-4-422-2-222-24-4-2-222-22-22000000000000-22000000000000000000000000000000000000
χ694-44-4-44-44-244-4-4-4-44422-2-222-2-44-2-2222-22-20000000000002-2000000000000000000000000000000000000
χ704-44-4-44-44-2-4-44444-4-422-2-222-2-4422-2-2-22-220000000000002-2000000000000000000000000000000000000
χ714-44-4-44-44-2-4-444-4-44422-2-222-24-422-2-22-22-2000000000000-22000000000000000000000000000000000000
χ724-4-4444-4-444i−4i−4i4i0000-44-444-4-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ734-4-4444-4-44−4i4i4i−4i0000-44-444-4-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ744-4-4444-4-4-24i−4i−4i4i00002-22-2-22200−2i2i2i−2i000000000000−2i32i30000000000000023−23000000000000000000000000
χ754-4-4444-4-4-24i−4i−4i4i00002-22-2-22200−2i2i2i−2i0000000000002i3−2i300000000000000−2323000000000000000000000000
χ764-4-4444-4-4-2−4i4i4i−4i00002-22-2-222002i−2i−2i2i000000000000−2i32i300000000000000−2323000000000000000000000000
χ774-4-4444-4-4-2−4i4i4i−4i00002-22-2-222002i−2i−2i2i0000000000002i3−2i30000000000000023−23000000000000000000000000
χ784-4-4-44-44440000-444-4-44-4-4-444000000-444-400000000000000000000000000000000000000000000000000
χ794-4-4-44-444-200004-4-442-2222-2-2000000-222-200004-4000000000000-22-220000000000000000000000000000
χ804-4-4-44-444-200004-4-442-2222-2-2000000-222-20000-440000000000002-22-20000000000000000000000000000
χ814-4-4-44-444-20000-444-42-2222-2-20000002-2-22000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ824-4-4-44-444-20000-444-42-2222-2-20000002-2-220000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ83888-88-8-8-8-400000000-4-4-44444000000000000000000000000000000000000000000000000000000000000
χ848-888-8-88-8-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000

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