Finite Group Databasebeta

← Group #10868035

Character table — Group #10868035

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222222234444444466666664444441212121212121212244444661212121212121212121212121212121244448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-111111111-1-11111-1-111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ91111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ101111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-1-1-111
χ111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-11-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-1111111-1-111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-11111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111111-111-1-1-1-111-1-111-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-111
χ17222222222-22222-2-2-2222222222-2-222-2-2-2-22222-2-20000-2-2-2-22222-2-2000000000000000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-2222222000022-2-2-2-2-2-222000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22-20000222222-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-220000-2-222-2-22222000000000000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-2-2222211-1-1111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-211-1-11111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-2222-2-21111-1-111-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-22-2-2221111-1-111-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111112-222-2-2-1-11111-1-111-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111112-2-2-222-1-11111-1-1111111-1-1-1-10000000000002-2-1-1110000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-1-2-200001111-1-1-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-1-2-200001111-1-1-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1220000-1-1111111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1220000-1-1111111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2111111112-20000-1-1-1-1-1-11111−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2111111112-20000-1-1-1-1-1-11111i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-22000011-1-111-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-22000011-1-111-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3722-2-2-22-22222i2i−2i−2i-2-222-2-22-2-22002i−2i0022-2-22i2i−2i−2i000000002i−2i00000000000000000000000000000000002i−2i2-20000
χ3822-2-2-22-22222i2i−2i−2i-2-222-2-22-2-22002i−2i0022-2-22i2i−2i−2i000000002i−2i0000000000000000000000000000000000−2i2i-220000
χ3922-2-2-22-2222−2i−2i2i2i-2-222-2-22-2-2200−2i2i0022-2-2−2i−2i2i2i00000000−2i2i00000000000000000000000000000000002i−2i-220000
χ4022-2-2-22-2222−2i−2i2i2i-2-222-2-22-2-2200−2i2i0022-2-2−2i−2i2i2i00000000−2i2i0000000000000000000000000000000000−2i2i2-20000
χ4122-2-2-22-222-22i2i−2i−2i22-22-2-22-2-2200−2i2i00-2-2222i2i−2i−2i00000000−2i2i000000000000002i2i−2i−2i000000000000002-200000000
χ4222-2-2-22-222-22i2i−2i−2i22-22-2-22-2-2200−2i2i00-2-2222i2i−2i−2i00000000−2i2i00000000000000−2i−2i2i2i00000000000000-2200000000
χ4322-2-2-22-222-2−2i−2i2i2i22-22-2-22-2-22002i−2i00-2-222−2i−2i2i2i000000002i−2i000000000000002i2i−2i−2i00000000000000-2200000000
χ4422-2-2-22-222-2−2i−2i2i2i22-22-2-22-2-22002i−2i00-2-222−2i−2i2i2i000000002i−2i00000000000000−2i−2i2i2i000000000000002-200000000
χ452-222-22-2-22-200002-22-22-222-2-20000002-22-2000000002i−2i000000000000002i−2i2i−2i2i−2i2i−2i000022-2-20000000000000000
χ462-222-22-2-22-200002-22-22-222-2-20000002-22-2000000002i−2i000000000000002i−2i2i−2i−2i2i−2i2i0000-2-2220000000000000000
χ472-222-22-2-22-200002-22-22-222-2-20000002-22-200000000−2i2i00000000000000−2i2i−2i2i2i−2i2i−2i0000-2-2220000000000000000
χ482-222-22-2-22-200002-22-22-222-2-20000002-22-200000000−2i2i00000000000000−2i2i−2i2i−2i2i−2i2i000022-2-20000000000000000
χ492-22-22-2-22202i−2i2i−2i000-222-2-2-222-2002i−2i00002i−2i2i−2i00000000002-22i−2i00000000000000−i2−i2i2i22−22−2000000000000−i2i22−2
χ502-22-22-2-22202i−2i2i−2i000-222-2-2-222-2002i−2i00002i−2i2i−2i00000000002-22i−2i00000000000000i2i2−i2−i2−22−22000000000000i2−i2−22
χ512-22-22-2-22202i−2i2i−2i000-222-2-2-22-2200−2i2i00002i−2i2i−2i0000000000-22−2i2i00000000000000−i2−i2i2i22−22−2000000000000i2−i2−22
χ522-22-22-2-22202i−2i2i−2i000-222-2-2-22-2200−2i2i00002i−2i2i−2i0000000000-22−2i2i00000000000000i2i2−i2−i2−22−22000000000000−i2i22−2
χ532-22-22-2-2220−2i2i−2i2i000-222-2-2-222-200−2i2i0000−2i2i−2i2i00000000002-2−2i2i00000000000000−i2−i2i2i2−22−22000000000000−i2i2−22
χ542-22-22-2-2220−2i2i−2i2i000-222-2-2-222-200−2i2i0000−2i2i−2i2i00000000002-2−2i2i00000000000000i2i2−i2−i22−22−2000000000000i2−i22−2
χ552-22-22-2-2220−2i2i−2i2i000-222-2-2-22-22002i−2i0000−2i2i−2i2i0000000000-222i−2i00000000000000−i2−i2i2i2−22−22000000000000i2−i22−2
χ562-22-22-2-2220−2i2i−2i2i000-222-2-2-22-22002i−2i0000−2i2i−2i2i0000000000-222i−2i00000000000000i2i2−i2−i22−22−2000000000000−i2i2−22
χ572-2-2-2222-22200002-2-2-2-222-22-2000000-222-20000002i−2i0000000000002i−2i2i−2i00002-2-222i−2i2i−2i00000000000000000000
χ582-2-2-2222-22200002-2-2-2-222-22-2000000-222-20000002i−2i0000000000002i−2i2i−2i0000-222-2−2i2i−2i2i00000000000000000000
χ592-2-2-2222-22200002-2-2-2-222-22-2000000-222-2000000−2i2i000000000000−2i2i−2i2i00002-2-22−2i2i−2i2i00000000000000000000
χ602-2-2-2222-22200002-2-2-2-222-22-2000000-222-2000000−2i2i000000000000−2i2i−2i2i0000-222-22i−2i2i−2i00000000000000000000
χ61444-4-4-44-440000000044-4-4-44-4000000000000000000000000000000000000000000000022−22−22220000000000000000
χ62444-4-4-44-440000000044-4-4-44-40000000000000000000000000000000000000000000000−222222−220000000000000000
χ6344-444-4-4-44000000004-44-44-4-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ6444-444-4-4-44000000004-44-44-4-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ6544-4-4-44-44-244i4i−4i−4i-4-44-222-222-2004i−4i00-2-222−2i−2i2i2i00000000−2i2i000000000000000000000000000000000000000000
χ6644-4-4-44-44-24−4i−4i4i4i-4-44-222-222-200−4i4i00-2-2222i2i−2i−2i000000002i−2i000000000000000000000000000000000000000000
χ6744-4-4-44-44-2-44i4i−4i−4i44-4-222-222-200−4i4i0022-2-2−2i−2i2i2i000000002i−2i000000000000000000000000000000000000000000
χ6844-4-4-44-44-2-4−4i−4i4i4i44-4-222-222-2004i−4i0022-2-22i2i−2i−2i00000000−2i2i000000000000000000000000000000000000000000
χ694-444-44-4-4440000-44-4-44-444-4-4000000-44-4400000000000000000000000000000000000000000000000000000000
χ704-444-44-4-4-240000-44-42-22-2-2220000002-22-200000000000000000000000023−23−23230000000000000000000000000000
χ714-444-44-4-4-240000-44-42-22-2-2220000002-22-2000000000000000000000000−232323−230000000000000000000000000000
χ724-444-44-4-4-2-400004-442-22-2-222000000-22-22000000004i−4i00000000000000−2i2i−2i2i0000000000000000000000000000
χ734-444-44-4-4-2-400004-442-22-2-222000000-22-2200000000−4i4i000000000000002i−2i2i−2i0000000000000000000000000000
χ744-44-44-4-44-204i−4i4i−4i0002-2-2222-24-4004i−4i0000−2i2i−2i2i0000000000-22−2i2i00000000000000000000000000000000000000
χ754-44-44-4-44-204i−4i4i−4i0002-2-2222-2-4400−4i4i0000−2i2i−2i2i00000000002-22i−2i00000000000000000000000000000000000000
χ764-44-44-4-44-20−4i4i−4i4i0002-2-2222-24-400−4i4i00002i−2i2i−2i0000000000-222i−2i00000000000000000000000000000000000000
χ774-44-44-4-44-20−4i4i−4i4i0002-2-2222-2-44004i−4i00002i−2i2i−2i00000000002-2−2i2i00000000000000000000000000000000000000
χ784-4-44-4-444404-4-44000-4-4-4-444400000000004-4-440000000000000000000000000000000000000000000000000000
χ794-4-44-4-44440-444-4000-4-4-4-44440000000000-444-40000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-204-4-440002222-2-2-20000000000-222-2000000−2i32i3000000−2i32i3000000000000000000000000000000000000
χ814-4-44-4-444-204-4-440002222-2-2-20000000000-222-20000002i3−2i30000002i3−2i3000000000000000000000000000000000000
χ824-4-44-4-444-20-444-40002222-2-2-200000000002-2-22000000−2i32i30000002i3−2i3000000000000000000000000000000000000
χ834-4-44-4-444-20-444-40002222-2-2-200000000002-2-220000002i3−2i3000000−2i32i3000000000000000000000000000000000000
χ844-4-4-4444-44-40000-444-4-444-44-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2400004-4-422-2-22-220000002-2-220000004i−4i000000000000−2i2i−2i2i00000000000000000000000000000000
χ864-4-4-4444-4-2400004-4-422-2-22-220000002-2-22000000−4i4i0000000000002i−2i2i−2i00000000000000000000000000000000
χ874-4-4-4444-4-2-40000-44422-2-22-22000000-222-20000000000000000000023−23−232300000000000000000000000000000000
χ884-4-4-4444-4-2-40000-44422-2-22-22000000-222-200000000000000000000−232323−2300000000000000000000000000000000
χ89888-8-8-88-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-888-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000

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