Finite Group Databasebeta

← Group #10944269

Character table — Group #10944269

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444444446666666688888888888812121212121212121212121216161616161616161616161648484848
order1222222234444666666622448888888812121212222244446612122424242424242424224488888888444412121212121212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-111-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1111-11-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-11-11
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1111-1-1-1-111-11-11
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-11111-1-11-11-1
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-22222-2-2-2-222-2-20000000022-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-2-2-2222222-2-200000000-2-222000000000000000000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-22222-2-2-2-2-2-22200000000-2-222000000000000000000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-2-2-22222-2-2220000000022-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-1111111110000000000002-22-2-1-111-1-1110000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000-1-1-1-111111111000000000000-22-2211-1-111-1-10000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000001111-1-1-1-1111100000000000022-2-2-1-1-1-111110000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000001111-1-1-1-11111000000000000-2-2221111-1-1-1-10000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-10000000011111111-1-1-1-10000000000002-2-22-1-11111-1-10000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-10000000011111111-1-1-1-1000000000000-222-211-1-1-1-1110000
χ2922-2-2-22-22222-2-22-2-22-2-22000000002i2i−2i−2i22-2-200000000000000002i2i−2i−2i2-22-22i2i−2i−2i00000000000000000000
χ3022-2-2-22-22222-2-22-2-22-2-22000000002i2i−2i−2i22-2-200000000000000002i2i−2i−2i-22-22−2i−2i2i2i00000000000000000000
χ3122-2-2-22-22222-2-22-2-22-2-2200000000−2i−2i2i2i22-2-20000000000000000−2i−2i2i2i2-22-2−2i−2i2i2i00000000000000000000
χ3222-2-2-22-22222-2-22-2-22-2-2200000000−2i−2i2i2i22-2-20000000000000000−2i−2i2i2i-22-222i2i−2i−2i00000000000000000000
χ3322-2-2-22-222-2-2222-2-22-2-22000022-2-20000-2-22200000000000022-2-200002-2-22000022-2-20000000000000000
χ3422-2-2-22-222-2-2222-2-22-2-22000022-2-20000-2-22200000000000022-2-20000-222-20000-2-2220000000000000000
χ3522-2-2-22-222-2-2222-2-22-2-220000-2-2220000-2-222000000000000-2-22200002-2-220000-2-2220000000000000000
χ3622-2-2-22-222-2-2222-2-22-2-220000-2-2220000-2-222000000000000-2-2220000-222-2000022-2-20000000000000000
χ372-22-2-2-22222-22-2-2222-2-2-22-22-2000000002-22-2000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ382-22-2-2-22222-22-2-2222-2-2-22-22-2000000002-22-2000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ392-22-2-2-22222-22-2-2222-2-2-2-22-22000000002-22-200000000-22-220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402-22-2-2-22222-22-2-2222-2-2-2-22-22000000002-22-200000000-22-22000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412-22-2-2-2222-22-22-2222-2-2-22-2-222-22-22-22-2-22-22000000002-2-222-22-22-22-20000000000000000000000000000
χ422-22-2-2-2222-22-22-2222-2-2-22-2-22-22-22-22-22-22-22000000002-2-22-22-22-22-220000000000000000000000000000
χ432-22-2-2-2222-22-22-2222-2-2-2-222-22-22-2-22-22-22-2200000000-222-22-22-2-22-220000000000000000000000000000
χ442-22-2-2-2222-22-22-2222-2-2-2-222-2-22-222-22-2-22-2200000000-222-2-22-222-22-20000000000000000000000000000
χ452-22-2-2-222-1-22-221-1-1-11112-2-222-22-22-22-21-11-100000000-111-1-11-11-11-1100000000000000003−33−33−33−30000
χ462-22-2-2-222-1-22-221-1-1-11112-2-222-22-22-22-21-11-100000000-111-1-11-11-11-110000000000000000−33−33−33−330000
χ472-22-2-2-222-1-22-221-1-1-11112-2-22-22-22-22-221-11-100000000-111-11-11-11-11-100000000000000003−3−333−3−330000
χ482-22-2-2-222-1-22-221-1-1-11112-2-22-22-22-22-221-11-100000000-111-11-11-11-11-10000000000000000−333−3−333−30000
χ492-22-2-2-222-1-22-221-1-1-1111-222-22-22-2-22-221-11-1000000001-1-11-11-111-11-100000000000000003−33−3−33−330000
χ502-22-2-2-222-1-22-221-1-1-1111-222-22-22-2-22-221-11-1000000001-1-11-11-111-11-10000000000000000−33−333−33−30000
χ512-22-2-2-222-1-22-221-1-1-1111-222-2-22-222-22-21-11-1000000001-1-111-11-1-11-1100000000000000003−3−33−333−30000
χ522-22-2-2-222-1-22-221-1-1-1111-222-2-22-222-22-21-11-1000000001-1-111-11-1-11-110000000000000000−333−33−3−330000
χ532-2-222-2-2222-2-22-2-2-2222-200002-2-2200002-2-2222-2-222-2-200002-2-22000000002-2-2200000000000000000000
χ542-2-222-2-2222-2-22-2-2-2222-200002-2-2200002-2-22-2-222-2-22200002-2-2200000000-222-200000000000000000000
χ552-2-222-2-2222-2-22-2-2-2222-20000-222-200002-2-2222-2-222-2-20000-222-200000000-222-200000000000000000000
χ562-2-222-2-2222-2-22-2-2-2222-20000-222-200002-2-22-2-222-2-2220000-222-2000000002-2-2200000000000000000000
χ572-2-222-2-222-222-2-2-2-2222-2000000002i−2i−2i2i-222-222-2-2-2-222000000002i−2i−2i2i000000002i−2i−2i2i0000000000000000
χ582-2-222-2-222-222-2-2-2-2222-2000000002i−2i−2i2i-222-2-2-22222-2-2000000002i−2i−2i2i00000000−2i2i2i−2i0000000000000000
χ592-2-222-2-222-222-2-2-2-2222-200000000−2i2i2i−2i-222-222-2-2-2-22200000000−2i2i2i−2i00000000−2i2i2i−2i0000000000000000
χ602-2-222-2-222-222-2-2-2-2222-200000000−2i2i2i−2i-222-2-2-22222-2-200000000−2i2i2i−2i000000002i−2i−2i2i0000000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400000000222200000000-2-222000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000000022220000000022-2-2000000000000000000000000000000000000
χ634444-4-4-4-44000044-4-44-4-400000000000000004-44-400000000000000000000000000000000000000000000
χ644444-4-4-4-44000044-4-44-4-40000000000000000-44-4400000000000000000000000000000000000000000000
χ6544-4-44-44-4400004-44-4-44-4000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ6644-4-44-44-4400004-44-4-44-400000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6744-4-4-44-44-244-4-4-222-222-2000000004i4i−4i−4i-2-2220000000000000000−2i−2i2i2i0000000000000000000000000000
χ6844-4-4-44-44-244-4-4-222-222-200000000−4i−4i4i4i-2-22200000000000000002i2i−2i−2i0000000000000000000000000000
χ6944-4-4-44-44-2-4-444-222-222-2000044-4-4000022-2-2000000000000-2-22200000000000000000000000000000000
χ7044-4-4-44-44-2-4-444-222-222-20000-4-444000022-2-200000000000022-2-200000000000000000000000000000000
χ714-44-444-4-440000-44-4-4-444000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ724-44-444-4-440000-44-4-4-44400000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ734-44-4-4-444-24-44-42-2-2-22224-44-400000000-22-2200000000-22-22000000000000000000000000000000000000
χ744-44-4-4-444-24-44-42-2-2-2222-44-4400000000-22-22000000002-22-2000000000000000000000000000000000000
χ754-4-444-4-44-24-4-44222-2-2-2200004-4-440000-222-2000000000000-222-200000000000000000000000000000000
χ764-4-444-4-44-24-4-44222-2-2-220000-444-40000-222-20000000000002-2-2200000000000000000000000000000000
χ774-4-444-4-44-2-444-4222-2-2-22000000004i−4i−4i4i2-2-220000000000000000−2i2i2i−2i0000000000000000000000000000
χ784-4-444-4-44-2-444-4222-2-2-2200000000−4i4i4i−4i2-2-2200000000000000002i−2i−2i2i0000000000000000000000000000
χ794-4-44-444-440000-4-44-44-4400000000000000004-4-4400000000000000000000000000000000000000000000
χ804-4-44-444-440000-4-44-44-440000000000000000-444-400000000000000000000000000000000000000000000
χ818888-8-8-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8288-8-88-88-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000
χ838-88-888-8-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

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