Finite Group Databasebeta

← Group #10830941

Character table — Group #10830941

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222222222223444466666664466661212121222222444666666666612121212121212128888888844121212122222888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-11-1-111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-11-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-11111-1-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1111-1-11-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-111-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-2000022-2-2000000002222-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-20000-2-22200000000-2-2-2-222-2-222000000000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111-1-11100000000-2-211110000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-100000000-2-211110000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111-1-1110000000022-1-1-1-10000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111000022-2-2−i3−i3i3i3−i3−i3i3i3-1-1-1-11111110000000000−i3i3−i3i30000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111000022-2-2i3i3−i3−i3i3i3−i3−i3-1-1-1-11111110000000000i3−i3i3−i30000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-111110000-2-222−i3−i3i3i3−i3−i3i3i31111-1-111-1-10000000000i3−i3i3−i30000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-1-111110000-2-222i3i3−i3−i3i3i3−i3−i31111-1-111-1-10000000000−i3i3−i3i30000000000
χ2722222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-200002-22-20000000022-2-22222-2-2000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-20000-22-2200000000-2-222-2-22222000000000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-22-2-22-1-1-1-11111-1-1111111-1-1000000002-2-1-1110000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-222-2-1-1-1-1111111-1-1-1-1111100000000-2211-1-10000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2222-2-221111-1-1-1-1-1-1111111-1-100000000-2211-1-10000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-222-222-21111-1-1-1-111-1-1-1-11111000000002-2-1-1110000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1221111111100002-22-2−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-1110000000000−i3i3i3−i30000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1221111111100002-22-2i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-1110000000000i3−i3−i3i30000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122111111110000-22-22−i3−i3i3i3i3i3−i3−i311-1-111-1-1-1-10000000000i3−i3−i3i30000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122111111110000-22-22i3i3−i3−i3−i3−i3i3i311-1-111-1-1-1-10000000000−i3i3i3−i30000000000
χ37222-2-22-2-222-2-2222-2-2-2-222-2-222-222-2-222-2-200000000000000000000002-2000000000000000000002i−2i2i−2i00
χ38222-2-22-2-222-2-2222-2-2-2-222-2-222-222-2-222-2-200000000000000000000002-200000000000000000000−2i2i−2i2i00
χ39222-2-22-2-222-2-22-2-222-2-222-2-22-2222-2-2-2-2220000000000000000000000-220022-2-222-2-20000000000000000
χ40222-2-22-2-222-2-22-2-222-2-222-2-22-2222-2-2-2-2220000000000000000000000-2200-2-222-2-2220000000000000000
χ41222-2-22-2-2-2-222222-2-2-2-222-2-22-22-2-22222-2-20000000000000000000000-22000000000000000000002i−2i−2i2i00
χ42222-2-22-2-2-2-222222-2-2-2-222-2-22-22-2-22222-2-20000000000000000000000-2200000000000000000000−2i2i2i−2i00
χ43222-2-22-2-2-2-2222-2-222-2-222-2-222-2-2-222-2-22200000000000000000000002-20022-2-2-2-2220000000000000000
χ44222-2-22-2-2-2-2222-2-222-2-222-2-222-2-2-222-2-22200000000000000000000002-200-2-22222-2-20000000000000000
χ452-2-22-222-2000022-2-222-2-2-22-220000002-22-2002-2000000002-22-2000000000000002-22-20000002-200000000
χ462-2-22-222-2000022-2-222-2-2-22-220000002-22-2002-2000000002-22-200000000000000-22-22000000-2200000000
χ472-2-22-222-2000022-2-222-2-2-22-220000002-22-200-2200000000-22-22000000000000002-22-2000000-2200000000
χ482-2-22-222-2000022-2-222-2-2-22-220000002-22-200-2200000000-22-2200000000000000-22-220000002-200000000
χ492-2-2-222-2200002-22-22-22-2-2-222000000-222-22-20000002-22-20000000000000000002-2-22000000002-2000000
χ502-2-2-222-2200002-22-22-22-2-2-222000000-222-22-20000002-22-2000000000000000000-222-200000000-22000000
χ512-2-2-222-2200002-22-22-22-2-2-222000000-222-2-22000000-22-220000000000000000002-2-2200000000-22000000
χ522-2-2-222-2200002-22-22-22-2-2-222000000-222-2-22000000-22-22000000000000000000-222-2000000002-2000000
χ53444-4-44-4-444-4-4-244-4-422-2-222-24-4-2-222-2-2220000000000000000000000-2200000000000000000000000000
χ54444-4-44-4-444-4-4-2-4-44422-2-222-2-44-2-22222-2-200000000000000000000002-200000000000000000000000000
χ55444-4-44-4-4-4-444-244-4-422-2-222-2-4422-2-2-2-22200000000000000000000002-200000000000000000000000000
χ56444-4-44-4-4-4-444-2-4-44422-2-222-24-422-2-222-2-20000000000000000000000-2200000000000000000000000000
χ5744-444-4-4-44-44-440000-4-44-444-4004-44-4000000000000000000000000000000000000000000000000000000
χ5844-444-4-4-44-44-4-2000022-22-2-2200-22-2200000000000000000000−2i32i3−2i32i3000000000000000000000000000000
χ5944-444-4-4-44-44-4-2000022-22-2-2200-22-22000000000000000000002i3−2i32i3−2i3000000000000000000000000000000
χ6044-444-4-4-4-44-4440000-4-44-444-400-44-44000000000000000000000000000000000000000000000000000000
χ6144-444-4-4-4-44-44-2000022-22-2-22002-22-200000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ6244-444-4-4-4-44-44-2000022-22-2-22002-22-2000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ6344-4-4-4-4444-4-4440000444-4-4-4-4004-4-44000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-44-20000-2-2-2222200-222-200000000000000000000000023−230023−23000000000000000000000000
χ6544-4-4-4-4444-4-44-20000-2-2-2222200-222-2000000000000000000000000−232300−2323000000000000000000000000
χ6644-4-4-4-444-444-440000444-4-4-4-400-444-4000000000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-444-4-20000-2-2-22222002-2-2200000000000000000000000023−2300−2323000000000000000000000000
χ6844-4-4-4-444-444-4-20000-2-2-22222002-2-22000000000000000000000000−23230023−23000000000000000000000000
χ694-444-4-4-44000040000-44-444-4-400000000000000000000000000000000000022−2222−2200000000000000000000
χ704-444-4-4-44000040000-44-444-4-4000000000000000000000000000000000000−2222−222200000000000000000000
χ714-44-44-44-40000400004-4-44-44-400000000000000000000000000000000000022−22−222200000000000000000000
χ724-44-44-44-40000400004-4-44-44-4000000000000000000000000000000000000−222222−2200000000000000000000
χ734-4-44-444-400004-444-44-4-4-44-44000000-44-4400000000000000000000000000000000000000000000000000
χ744-4-44-444-40000-24-4-44-2222-22-2000000-22-22004-400000000-22-220000000000000000000000000000000000
χ754-4-44-444-40000-24-4-44-2222-22-2000000-22-2200-44000000002-22-20000000000000000000000000000000000
χ764-4-44-444-40000-2-444-4-2222-22-20000002-22-2000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ774-4-44-444-40000-2-444-4-2222-22-20000002-22-20000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ784-4-4-444-44000044-44-4-44-4-4-4440000004-4-4400000000000000000000000000000000000000000000000000
χ794-4-4-444-440000-24-44-42-2222-2-2000000-222-200000000−2i32i32i3−2i300000000000000000000000000000000000000
χ804-4-4-444-440000-24-44-42-2222-2-2000000-222-2000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ814-4-4-444-440000-2-44-442-2222-2-20000002-2-224-4000000-22-2200000000000000000000000000000000000000
χ824-4-4-444-440000-2-44-442-2222-2-20000002-2-22-440000002-22-200000000000000000000000000000000000000
χ838-888-8-8-880000-400004-44-4-444000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-80000-40000-444-44-44000000000000000000000000000000000000000000000000000000000000

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