Finite Group Databasebeta

← Group #10849335

Character table — Group #10849335

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124444441212121212121212121212121212121212124444441212121222224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-111-1-1111111111111-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-1111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1
χ911111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-111-1-1-1-111-1-111111-111-1-1-1-1-1-11111-1-111-1-1
χ1011111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-111-1-11111-1-1-1-111-1-111
χ1111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-111-1-11111-11-1-111-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-11-1-1111111-1-111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-1-1-111-1-1-1-1111111-11-1-111-1-111-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-11111111-111-1-1-1-111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11-111-1-111-1-11111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222200002-2000000002222-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-222-2-2-2-222220000-2200000000-2-2-2-2-2-22222000000000000000000000000
χ19222222222-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-20000-2-20000000022-2-222-2-222000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222-2-2-2-2-2-2-2-2-2-200002200000000-2-2222222-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-11111-1-111110000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111-1-11111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1111122-2-2-22-1-1-1-11111-1-11111-1-11100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-11111-2-222-221111-1-1-1-1-1-11111-1-1110000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-1111122-2-22-2-1-1-1-1111111-1-11111-1-10000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1-1-11111-2-2222-21111-1-1-1-111-1-11111-1-100002-2-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-100002-2−i3−i3i3i3−i3−i3i3i3-1-1-1-1111111000000−i3i3−i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-1-1-1-100002-2i3i3−i3−i3i3i3−i3−i3-1-1-1-1111111000000i3−i3i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-10000-22−i3−i3i3i3−i3−i3i3i3111111-1-1-1-1000000i3−i3i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2221111-1-1-1-10000-22i3i3−i3−i3i3i3−i3−i3111111-1-1-1-1000000−i3i3−i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2222222111111110000-2-2−i3−i3i3i3i3i3−i3−i3-1-111-1-111-1-1000000−i3i3i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2222222111111110000-2-2i3i3−i3−i3−i3−i3i3i3-1-111-1-111-1-1000000i3−i3−i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-211111111000022−i3−i3i3i3i3i3−i3−i311-1-1-1-1-1-111000000i3−i3−i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-211111111000022i3i3−i3−i3−i3−i3i3i311-1-1-1-1-1-111000000−i3i3i3−i300000000000000
χ3722-22-2-22-22-22-222-222-2-2-20000000022-2-20000002-20000002-22-200000000002i2i−2i−2i000000000000002i−2i0000
χ3822-22-2-22-22-22-222-222-2-2-20000000022-2-20000002-20000002-22-20000000000−2i−2i2i2i00000000000000−2i2i0000
χ3922-22-2-22-22-22-222-222-2-2-20000000022-2-2000000-22000000-22-2200000000002i2i−2i−2i00000000000000−2i2i0000
χ4022-22-2-22-22-22-222-222-2-2-20000000022-2-2000000-22000000-22-220000000000−2i−2i2i2i000000000000002i−2i0000
χ412-22-22-22-22-2-222-222-22-2-2000000002-22-200002-200002-22-2000000000000002i−2i2i−2i0000000000002i−2i000000
χ422-22-22-22-22-2-222-222-22-2-2000000002-22-200002-200002-22-200000000000000−2i2i−2i2i000000000000−2i2i000000
χ432-22-22-22-22-2-222-222-22-2-2000000002-22-20000-220000-22-22000000000000002i−2i2i−2i000000000000−2i2i000000
χ442-22-22-22-22-2-222-222-22-2-2000000002-22-20000-220000-22-2200000000000000−2i2i−2i2i0000000000002i−2i000000
χ452-2-2-2-222222-2-22-2-22-2-2222-2002-2002-2-2222-2-20000000000000000002-200002-2-220000002-2000000000000
χ462-2-2-2-222222-2-22-2-22-2-2222-2002-2002-2-2222-2-20000000000000000002-20000-222-2000000-22000000000000
χ472-2-2-2-222222-2-22-2-22-2-222-2200-22002-2-22-2-222000000000000000000-2200002-2-22000000-22000000000000
χ482-2-2-2-222222-2-22-2-22-2-222-2200-22002-2-22-2-222000000000000000000-220000-222-20000002-2000000000000
χ492-2-2-2-22222-222-2-2-22-2-2222-200-2200-222-222-2-2000000000000000000-2200000000000000002-22-200000000
χ502-2-2-2-22222-222-2-2-22-2-2222-200-2200-222-222-2-2000000000000000000-220000000000000000-22-2200000000
χ512-2-2-2-22222-222-2-2-22-2-222-22002-200-222-2-2-2220000000000000000002-200000000000000002-2-2200000000
χ522-2-2-2-22222-222-2-2-22-2-222-22002-200-222-2-2-2220000000000000000002-20000000000000000-222-200000000
χ53444-4-44-4-44000044-4-4-44-4004-4000000000000000000000000004-400000000000000000000000000000000
χ54444-4-44-4-44000044-4-4-44-400-4400000000000000000000000000-4400000000000000000000000000000000
χ55444-4-44-4-4-20000-2-2222-22004-400000000−2i32i3−2i32i300000000000000-22−2i32i3000000000000000000000000000000
χ56444-4-44-4-4-20000-2-2222-22004-4000000002i3−2i32i3−2i300000000000000-222i3−2i3000000000000000000000000000000
χ57444-4-44-4-4-20000-2-2222-2200-4400000000−2i32i3−2i32i3000000000000002-22i3−2i3000000000000000000000000000000
χ58444-4-44-4-4-20000-2-2222-2200-44000000002i3−2i32i3−2i3000000000000002-2−2i32i3000000000000000000000000000000
χ5944-44-4-44-444-44-44-444-4-4-400000000-4-4440000000000000000000000000000000000000000000000000000
χ6044-44-4-44-4-24-44-4-22-2-22220000000022-2-200000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ6144-44-4-44-4-24-44-4-22-2-22220000000022-2-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ6244-44-4-44-4-2-44-44-22-2-222200000000-2-2220000004-4000000-22-220000000000000000000000000000000000
χ6344-44-4-44-4-2-44-44-22-2-222200000000-2-222000000-440000002-22-20000000000000000000000000000000000
χ6444-4-44-4-44400004-4-4-44-440000000000000000000000000000000000000000000000000000000000000022−22
χ6544-4-44-4-44400004-4-4-44-4400000000000000000000000000000000000000000000000000000000000000−2222
χ664-444-4-4-4440000-44-44-4-4400000000000000000000000000000000000000000000000000000000000022−2200
χ674-444-4-4-4440000-44-44-4-44000000000000000000000000000000000000000000000000000000000000−222200
χ684-44-44-44-4444-4-4-444-44-4-400000000-44-440000000000000000000000000000000000000000000000000000
χ694-44-44-44-4-244-4-42-2-22-222000000002-22-20000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ704-44-44-44-4-244-4-42-2-22-222000000002-22-200000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ714-44-44-44-4-2-4-4442-2-22-22200000000-22-2200004-40000-22-2200000000000000000000000000000000000000
χ724-44-44-44-4-2-4-4442-2-22-22200000000-22-220000-4400002-22-200000000000000000000000000000000000000
χ734-4-4444-4-440000-4-4-4444-40000004i−4i0000000000000000000000000000004i−4i000000000000000000000000
χ744-4-4444-4-440000-4-4-4444-4000000−4i4i000000000000000000000000000000−4i4i000000000000000000000000
χ754-4-4444-4-4-20000222-2-2-220000004i−4i0000−2i32i32i3−2i30000000000000000000023−23−2i2i000000000000000000000000
χ764-4-4444-4-4-20000222-2-2-220000004i−4i00002i3−2i3−2i32i300000000000000000000−2323−2i2i000000000000000000000000
χ774-4-4444-4-4-20000222-2-2-22000000−4i4i0000−2i32i32i3−2i300000000000000000000−23232i−2i000000000000000000000000
χ784-4-4444-4-4-20000222-2-2-22000000−4i4i00002i3−2i3−2i32i30000000000000000000023−232i−2i000000000000000000000000
χ794-4-4-4-4444-24-4-4422-222-2-24-4004-400-222-2-2-222000000000000000000-220000000000000000000000000000
χ804-4-4-4-4444-24-4-4422-222-2-2-4400-4400-222-222-2-20000000000000000002-20000000000000000000000000000
χ814-4-4-4-4444-2-444-422-222-2-24-400-44002-2-22-2-2220000000000000000002-20000000000000000000000000000
χ824-4-4-4-4444-2-444-422-222-2-2-44004-4002-2-2222-2-2000000000000000000-220000000000000000000000000000
χ8388-8-88-8-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-400004-44-444-40000000000000000000000000000000000000000000000000000000000000000

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