Finite Group Databasebeta

← Group #10844794

Character table — Group #10844794

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222444444666612121212121212121212121212128888888844121212124444888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
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
χ911111111111-1-1-1-1111111111-1-11111-1-1-1-1111-1-1-11-11111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-111-1-11-1
χ1011111111111-1-1-1-1111111111-1-11111-1-1-1-1111-1-1-11-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-1-111-11
χ1111111111111-1-1-1-1111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-111-11
χ1211111111111-1-1-1-1111111111-1-11111-1-1-1-111-11-1-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-11111-1-11-1
χ1311111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-11-1-111-1-11111-1-1-11
χ1411111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-11-1111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-11-1-11111-1-1-1-1111-1
χ1511111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11-111-1-1-1-111-1-1111-1
χ1611111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111-111-1-111-1-111-1-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-2-22222002200-2-20000-2-222220000-2-2-2-2000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2222200-2-200220000-2-2-2-2-2-200002222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2002-200-2200002222-2-20000-2-222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200-22002-2000022-2-222000022-2-2000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-11111-1-1-1-1111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-1-11111-1-1-1-100000000-2-211110000000000
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
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111222-2-2-22-2-1-1-1-111-1-1111111-1-111000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-1111122-22-2-2-22-1-1-1-11111-1-1111111-1-100000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-22-2222-2111111-1-111-1-1-1-1-1-11100000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-2-2222-2211111111-1-1-1-1-1-111-1-1000000002-2-1-1110000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002200-2-2−i3−i3i3i311-1-1-1-1−i3−i3i3i311110000000000−i3i3−i3i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-1002200-2-2i3i3−i3−i311-1-1-1-1i3i3−i3−i311110000000000i3−i3i3−i30000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-2-20022−i3−i3i3i3111111−i3−i3i3i3-1-1-1-10000000000i3−i3i3−i30000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-21111-1-1-1-100-2-20022i3i3−i3−i3111111i3i3−i3−i3-1-1-1-10000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002-200-22−i3−i3i3i3-1-1-1-111i3i3−i3−i311-1-10000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111002-200-22i3i3−i3−i3-1-1-1-111−i3−i3i3i311-1-10000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-22002-2−i3−i3i3i3-1-111-1-1i3i3−i3−i3-1-1110000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100-22002-2i3i3−i3−i3-1-111-1-1−i3−i3i3i3-1-1110000000000−i3i3i3−i30000000000
χ37222-2-2-22-222-20000-2222-22-2-2-20022-2-200002-20000002-22-2000000000000002i2i−2i−2i00000000002i−2i00000000
χ38222-2-2-22-222-20000-2222-22-2-2-20022-2-200002-20000002-22-200000000000000−2i−2i2i2i0000000000−2i2i00000000
χ39222-2-2-22-222-20000-2222-22-2-2-20022-2-20000-22000000-22-22000000000000002i2i−2i−2i0000000000−2i2i00000000
χ40222-2-2-22-222-20000-2222-22-2-2-20022-2-20000-22000000-22-2200000000000000−2i−2i2i2i00000000002i−2i00000000
χ412-222-22-2-222222-2-2-2-2-2-2-222-222-22-22-222-2-20000000000002-20000000000002i−2i2i−2i2i2i−2i−2i0000000000000000
χ422-222-22-2-222222-2-2-2-2-2-2-222-222-22-22-222-2-20000000000002-2000000000000−2i2i−2i2i−2i−2i2i2i0000000000000000
χ432-222-22-2-2222-2-222-2-2-2-2-222-22-222-22-2-2-222000000000000-220000000000002i−2i2i−2i−2i−2i2i2i0000000000000000
χ442-222-22-2-2222-2-222-2-2-2-2-222-22-222-22-2-2-222000000000000-22000000000000−2i2i−2i2i2i2i−2i−2i0000000000000000
χ452-222-22-2-22-2-222-2-222-2-2-222-22-22-22-2222-2-2000000000000-220000000000000000000000000000002-22-200
χ462-222-22-2-22-2-222-2-222-2-2-222-22-22-22-2222-2-2000000000000-22000000000000000000000000000000-22-2200
χ472-222-22-2-22-2-2-2-22222-2-2-222-222-2-22-22-2-2220000000000002-20000000000000000000000000000002-2-2200
χ482-222-22-2-22-2-2-2-22222-2-2-222-222-2-22-22-2-2220000000000002-2000000000000000000000000000000-222-200
χ492-22-22-2-2222-200002-2-2-222-22-2002-2-22000000002i−2i0000000000002i−2i2i−2i00002-2-220000000000002i−2i000000
χ502-22-22-2-2222-200002-2-2-222-22-2002-2-22000000002i−2i0000000000002i−2i2i−2i0000-222-2000000000000−2i2i000000
χ512-22-22-2-2222-200002-2-2-222-22-2002-2-2200000000−2i2i000000000000−2i2i−2i2i00002-2-22000000000000−2i2i000000
χ522-22-22-2-2222-200002-2-2-222-22-2002-2-2200000000−2i2i000000000000−2i2i−2i2i0000-222-20000000000002i−2i000000
χ53444-4-4-44-44-4400004-444-44-4-4-400-4-444000000000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-24-40000-44-2-22-222200-2-22200004-4000000-22-2200000000000000000000000000000000000000
χ55444-4-4-44-4-24-40000-44-2-22-222200-2-2220000-440000002-22-200000000000000000000000000000000000000
χ56444-4-4-44-4-2-4400004-4-2-22-22220022-2-2000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ57444-4-4-44-4-2-4400004-4-2-22-22220022-2-20000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ5844-44-4-4-444000000004-44-44-4-40000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ5944-44-4-4-444000000004-44-44-4-400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6044-4-444-4-44004-44-4004-4-4-4-4440000004-44-400000000000000000000000000000000000000000000000000
χ6144-4-444-4-4400-44-44004-4-4-4-444000000-44-4400000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-2004-44-400-22222-2-2000000-22-220000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ6344-4-444-4-4-2004-44-400-22222-2-2000000-22-2200000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ6444-4-444-4-4-200-44-4400-22222-2-20000002-22-20000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ6544-4-444-4-4-200-44-4400-22222-2-20000002-22-200000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ664-444-44-4-4-24444-4-4-4-4222-2-22-24-4-22-22-2-222000000000000-22000000000000000000000000000000000000
χ674-444-44-4-4-244-4-444-4-4222-2-22-2-44-22-2222-2-20000000000002-2000000000000000000000000000000000000
χ684-444-44-4-4-2-4-444-4-444222-2-22-2-442-22-2-2-2220000000000002-2000000000000000000000000000000000000
χ694-444-44-4-4-2-4-4-4-44444222-2-22-24-42-22-222-2-2000000000000-22000000000000000000000000000000000000
χ704-44-44-4-444-440000-44-4-444-44-400-444-4000000000000000000000000000000000000000000000000000000
χ714-44-44-4-44-24-400004-422-2-22-2200-222-2000000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000
χ724-44-44-4-44-24-400004-422-2-22-2200-222-200000000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000
χ734-44-44-4-44-2-440000-4422-2-22-22002-2-22000000000000000000000023−23−23230000000000000000000000000000
χ744-44-44-4-44-2-440000-4422-2-22-22002-2-220000000000000000000000−232323−230000000000000000000000000000
χ754-4-444-44-4400000000-44-4-444-4000000000000000000000000000000000000000022−22−22220000000000000000
χ764-4-444-44-4400000000-44-4-444-40000000000000000000000000000000000000000−222222−220000000000000000
χ774-4-4-4-44444004-4-4400-444-4-4-440000004-4-4400000000000000000000000000000000000000000000000000
χ784-4-4-4-4444400-444-400-444-4-4-44000000-444-400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-2004-4-44002-2-2222-2000000-222-20000000000000023−2323−2300000000000000000000000000000000
χ804-4-4-4-4444-2004-4-44002-2-2222-2000000-222-200000000000000−2323−232300000000000000000000000000000000
χ814-4-4-4-4444-200-444-4002-2-2222-20000002-2-220000000000000023−23−232300000000000000000000000000000000
χ824-4-4-4-4444-200-444-4002-2-2222-20000002-2-2200000000000000−232323−2300000000000000000000000000000000
χ8388-88-8-8-88-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000

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