Finite Group Databasebeta

← Group #10945051

Character table — Group #10945051

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888121212121212121212121212121212121616161616161616161616162424242424242424
order1222222234444666666622444444444412121212661212121212121212121244444444444444444444121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-222000000000000000000000000000000000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-1-1-11111-1-11111000000000000000022-2-2-1-1-1-1111100000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-1-1-11111-1-111110000000000000000-2-2221111-1-1-1-100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-1-1-111-1-11111-1-11100000000000000002-22-2-1-111-1-11100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-222-2-2-2-2-1-1-1-111-1-11111-1-1110000000000000000-22-2211-1-111-1-100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-222-2-2-1-1-1-11111-1-11111-1-100000000000000002-2-22-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-222-2-2-1-1-1-11111-1-11111-1-10000000000000000-222-211-1-1-1-11100000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-222-2-21111-1-1-1-1111111-1-100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-222-2-21111-1-1-1-1111111-1-100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-2-2-21111-1-111-1-111-1-11100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-22222-2-2-2-21111-1-111-1-111-1-11100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222221111111111-1-1-1-1-1-100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22222221111111111-1-1-1-1-1-100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ3722-22-2-2-22222-2-22-22-2-22-200002i−2i002i−2i0022-2-200002i−2i00002i−2i00002i2i−2i−2i22-2-2000000000000000000000000
χ3822-22-2-2-22222-2-22-22-2-22-200002i−2i002i−2i0022-2-200002i−2i00002i−2i0000−2i−2i2i2i-2-222000000000000000000000000
χ3922-22-2-2-22222-2-22-22-2-22-20000−2i2i00−2i2i0022-2-20000−2i2i0000−2i2i00002i2i−2i−2i-2-222000000000000000000000000
χ4022-22-2-2-22222-2-22-22-2-22-20000−2i2i00−2i2i0022-2-20000−2i2i0000−2i2i0000−2i−2i2i2i22-2-2000000000000000000000000
χ4122-22-2-2-222-2-2222-22-2-22-200002i−2i00−2i2i00-2-22200002i−2i0000−2i2i2i2i−2i−2i0000000022-2-200000000000000000000
χ4222-22-2-2-222-2-2222-22-2-22-200002i−2i00−2i2i00-2-22200002i−2i0000−2i2i−2i−2i2i2i00000000-2-22200000000000000000000
χ4322-22-2-2-222-2-2222-22-2-22-20000−2i2i002i−2i00-2-2220000−2i2i00002i−2i2i2i−2i−2i00000000-2-22200000000000000000000
χ4422-22-2-2-222-2-2222-22-2-22-20000−2i2i002i−2i00-2-2220000−2i2i00002i−2i−2i−2i2i2i0000000022-2-200000000000000000000
χ452-22-22-2-2222-22-2-22-22-22-2002i−2i002i−2i00002-22-2002i−2i00002i−2i0000002i−2i2i−2i00002-22-200000000000000000000
χ462-22-22-2-2222-22-2-22-22-22-2002i−2i002i−2i00002-22-2002i−2i00002i−2i000000−2i2i−2i2i0000-22-2200000000000000000000
χ472-22-22-2-2222-22-2-22-22-22-200−2i2i00−2i2i00002-22-200−2i2i0000−2i2i0000002i−2i2i−2i0000-22-2200000000000000000000
χ482-22-22-2-2222-22-2-22-22-22-200−2i2i00−2i2i00002-22-200−2i2i0000−2i2i000000−2i2i−2i2i00002-22-200000000000000000000
χ492-22-22-2-222-22-22-22-22-22-2002i−2i00−2i2i0000-22-22002i−2i0000−2i2i002i−2i2i−2i00002-22-2000000000000000000000000
χ502-22-22-2-222-22-22-22-22-22-2002i−2i00−2i2i0000-22-22002i−2i0000−2i2i00−2i2i−2i2i0000-22-22000000000000000000000000
χ512-22-22-2-222-22-22-22-22-22-200−2i2i002i−2i0000-22-2200−2i2i00002i−2i002i−2i2i−2i0000-22-22000000000000000000000000
χ522-22-22-2-222-22-22-22-22-22-200−2i2i002i−2i0000-22-2200−2i2i00002i−2i00−2i2i−2i2i00002-22-2000000000000000000000000
χ532-2-2-2-222222-2-22-2-2-2-22222-2000000002-22-2-222-200002-200002-2-222-2-220000000000000000000000000000
χ542-2-2-2-222222-2-22-2-2-2-22222-2000000002-22-2-222-200002-20000-222-2-222-20000000000000000000000000000
χ552-2-2-2-222222-2-22-2-2-2-2222-2200000000-222-2-22-220000-2200002-2-22-222-20000000000000000000000000000
χ562-2-2-2-222222-2-22-2-2-2-2222-2200000000-222-2-22-220000-220000-222-22-2-220000000000000000000000000000
χ572-2-2-2-22222-222-2-2-2-2-22222-200000000-22-222-22-20000-220000000000002-2-22-222-200000000000000000000
χ582-2-2-2-22222-222-2-2-2-2-22222-200000000-22-222-22-20000-22000000000000-222-22-2-2200000000000000000000
χ592-2-2-2-22222-222-2-2-2-2-2222-22000000002-2-222-2-2200002-20000000000002-2-222-2-2200000000000000000000
χ602-2-2-2-22222-222-2-2-2-2-2222-22000000002-2-222-2-2200002-2000000000000-222-2-222-200000000000000000000
χ61444-4-4-44-44000044-4-4-4-440000000000000000000000000000000000000000000000000000000000000022−22
χ62444-4-4-44-44000044-4-4-4-4400000000000000000000000000000000000000000000000000000000000000−2222
χ6344-44-4-4-44-244-4-4-22-222-2200004i−4i004i−4i00-2-2220000−2i2i0000−2i2i000000000000000000000000000000000000
χ6444-44-4-4-44-244-4-4-22-222-220000−4i4i00−4i4i00-2-22200002i−2i00002i−2i000000000000000000000000000000000000
χ6544-44-4-4-44-2-4-444-22-222-2200004i−4i00−4i4i0022-2-20000−2i2i00002i−2i000000000000000000000000000000000000
χ6644-44-4-4-44-2-4-444-22-222-220000−4i4i004i−4i0022-2-200002i−2i0000−2i2i000000000000000000000000000000000000
χ6744-4-444-4-4400004-4-444-4-40000000000000000000000000000000000000000000000000000000022−22000000
χ6844-4-444-4-4400004-4-444-4-400000000000000000000000000000000000000000000000000000000−2222000000
χ694-444-44-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000000000022−220000
χ704-444-44-4-440000-444-44-4-40000000000000000000000000000000000000000000000000000000000−22220000
χ714-44-44-4-44-24-44-42-22-22-22004i−4i004i−4i0000-22-2200−2i2i0000−2i2i00000000000000000000000000000000000000
χ724-44-44-4-44-24-44-42-22-22-2200−4i4i00−4i4i0000-22-22002i−2i00002i−2i00000000000000000000000000000000000000
χ734-44-44-4-44-2-44-442-22-22-22004i−4i00−4i4i00002-22-200−2i2i00002i−2i00000000000000000000000000000000000000
χ744-44-44-4-44-2-44-442-22-22-2200−4i4i004i−4i00002-22-2002i−2i0000−2i2i00000000000000000000000000000000000000
χ754-4-444-44-440000-4-444-4-44000000000000000000000000000000000000000000000000000000000000−2i22i200
χ764-4-444-44-440000-4-444-4-440000000000000000000000000000000000000000000000000000000000002i2−2i200
χ774-4-4-4-4444-24-4-442222-2-2-24-4000000004-4-222-2-220000-220000000000000000000000000000000000000000
χ784-4-4-4-4444-24-4-442222-2-2-2-4400000000-44-222-22-200002-20000000000000000000000000000000000000000
χ794-4-4-4-4444-2-444-42222-2-2-24-400000000-442-2-22-2200002-20000000000000000000000000000000000000000
χ804-4-4-4-4444-2-444-42222-2-2-2-44000000004-42-2-222-20000-220000000000000000000000000000000000000000
χ81888-8-8-88-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000
χ8288-8-888-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000
χ838-888-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-88-8-4000044-4-444-40000000000000000000000000000000000000000000000000000000000000000

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