Finite Group Databasebeta

← Group #10858315

Character table — Group #10858315

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222344444444666666644444412121212121212122244446666121212121212121212121212121222228888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-11111111111-1-1111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-111-1-11111111111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ8111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-1-1-111
χ101111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-1111111-1-1
χ111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-111111-111-1-111-1-1-1-111-1-1
χ121111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11111-1-111
χ131111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-11-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-111-1-1
χ141111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-11-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111
χ151111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-11-1-111-1-111-1-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-11111-1-11111-1-1
χ17222222222-22222-2-2-2222222222-2-222-2-2-2-2222200-2-200000022-2-222-2-2-2-200000000000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-222220022000000-2-2-2-2-2-2222200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-200-220000002222-2-2-2-22200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2002-2000000-2-2222222-2-200000000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1-1-1-1-1-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-122-2-222-1-1-1-111-1-1111111-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111-1-1111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111222-2-2-2-1-1-1-1-1-11111-1-1111111000000000000-2211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-2-22-2221111-1-11111-1-111-1-1-1-10000000000002-2-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111122-22-2-2-1-1-1-11111-1-111-1-111110000000000002-2-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2-222211111111-1-111-1-1-1-1-1-1000000000000-2211-1-10000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-100-2-200−i3−i3i3i3-1-111-1-11111−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-100-2-200i3i3−i3−i3-1-111-1-11111i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002200−i3−i3i3i3111111-1-1-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002200i3i3−i3−i3111111-1-1-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200−i3−i3i3i3-1-1-1-11111-1-1i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200i3i3−i3−i3-1-1-1-11111-1-1−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111002-200−i3−i3i3i311-1-1-1-1-1-111i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111002-200i3i3−i3−i311-1-1-1-1-1-111−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ372222-2-2-2-22200002-2-2222-2-2-2-200000022-2-200002-200002-22-20000000000000022-2-222-2-200000000000000000000
χ382222-2-2-2-22200002-2-2222-2-2-2-200000022-2-200002-200002-22-200000000000000-2-222-2-22200000000000000000000
χ392222-2-2-2-22200002-2-2222-2-2-2-200000022-2-20000-220000-22-220000000000000022-2-2-2-22200000000000000000000
χ402222-2-2-2-22200002-2-2222-2-2-2-200000022-2-20000-220000-22-2200000000000000-2-22222-2-200000000000000000000
χ4122-2-22-22-2202i2i−2i−2i0002-2-2-222-22i−2i002-200002i2i−2i−2i00000000002i−2i002-20000000000002−22−2−i2−i2i2i20000000000002−2−i2i2
χ4222-2-22-22-2202i2i−2i−2i0002-2-2-222-22i−2i002-200002i2i−2i−2i00000000002i−2i002-2000000000000−22−22i2i2−i2−i2000000000000−22i2−i2
χ4322-2-22-22-2202i2i−2i−2i0002-2-2-222-2−2i2i00-2200002i2i−2i−2i0000000000−2i2i00-220000000000002−22−2−i2−i2i2i2000000000000−22i2−i2
χ4422-2-22-22-2202i2i−2i−2i0002-2-2-222-2−2i2i00-2200002i2i−2i−2i0000000000−2i2i00-22000000000000−22−22i2i2−i2−i20000000000002−2−i2i2
χ4522-2-22-22-220−2i−2i2i2i0002-2-2-222-22i−2i00-220000−2i−2i2i2i00000000002i−2i00-220000000000002−22−2i2i2−i2−i2000000000000−22−i2i2
χ4622-2-22-22-220−2i−2i2i2i0002-2-2-222-22i−2i00-220000−2i−2i2i2i00000000002i−2i00-22000000000000−22−22−i2−i2i2i20000000000002−2i2−i2
χ4722-2-22-22-220−2i−2i2i2i0002-2-2-222-2−2i2i002-20000−2i−2i2i2i0000000000−2i2i002-20000000000002−22−2i2i2−i2−i20000000000002−2i2−i2
χ4822-2-22-22-220−2i−2i2i2i0002-2-2-222-2−2i2i002-20000−2i−2i2i2i0000000000−2i2i002-2000000000000−22−22−i2−i2i2i2000000000000−22−i2i2
χ492-2-2222-2-2222i−2i2i−2i-2-22-2-222-22-2002i−2i002-22-22i−2i2i−2i0000000000002i−2i00000000000000000000000000002-22i−2i000000
χ502-2-2222-2-2222i−2i2i−2i-2-22-2-222-22-2002i−2i002-22-22i−2i2i−2i0000000000002i−2i0000000000000000000000000000-22−2i2i000000
χ512-2-2222-2-222−2i2i−2i2i-2-22-2-222-22-200−2i2i002-22-2−2i2i−2i2i000000000000−2i2i00000000000000000000000000002-2−2i2i000000
χ522-2-2222-2-222−2i2i−2i2i-2-22-2-222-22-200−2i2i002-22-2−2i2i−2i2i000000000000−2i2i0000000000000000000000000000-222i−2i000000
χ532-2-2222-2-22-22i−2i2i−2i22-2-2-222-22-200−2i2i00-22-222i−2i2i−2i000000000000−2i2i00000000002-22-20000000000000000002i−2i0000
χ542-2-2222-2-22-22i−2i2i−2i22-2-2-222-22-200−2i2i00-22-222i−2i2i−2i000000000000−2i2i0000000000-22-22000000000000000000−2i2i0000
χ552-2-2222-2-22-2−2i2i−2i2i22-2-2-222-22-2002i−2i00-22-22−2i2i−2i2i0000000000002i−2i00000000002-22-2000000000000000000−2i2i0000
χ562-2-2222-2-22-2−2i2i−2i2i22-2-2-222-22-2002i−2i00-22-22−2i2i−2i2i0000000000002i−2i0000000000-22-220000000000000000002i−2i0000
χ572-2-22-2-2222-200002-22-2-22-22-22000000-222-2000000002-2000000000000002-22-22-2-2200002-22-20000000000000000
χ582-2-22-2-2222-200002-22-2-22-22-22000000-222-2000000002-2000000000000002-22-2-222-20000-22-220000000000000000
χ592-2-22-2-2222-200002-22-2-22-22-22000000-222-200000000-2200000000000000-22-222-2-220000-22-220000000000000000
χ602-2-22-2-2222-200002-22-2-22-22-22000000-222-200000000-2200000000000000-22-22-222-200002-22-20000000000000000
χ614444-4-4-4-44-40000-444444-4-4-4-4000000-4-44400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-2400004-4-4-2-2-22222000000-2-22200004-40000-22-22000000000000000000000000000000000000000000
χ634444-4-4-4-4-2400004-4-4-2-2-22222000000-2-2220000-4400002-22-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-40000-444-2-2-2222200000022-2-20000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ654444-4-4-4-4-2-40000-444-2-2-2222200000022-2-200000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ6644-4-44-44-4-204i4i−4i−4i000-2222-2-224i−4i004-40000−2i−2i2i2i0000000000−2i2i00-22000000000000000000000000000000000000
χ6744-4-44-44-4-204i4i−4i−4i000-2222-2-22−4i4i00-440000−2i−2i2i2i00000000002i−2i002-2000000000000000000000000000000000000
χ6844-4-44-44-4-20−4i−4i4i4i000-2222-2-224i−4i00-4400002i2i−2i−2i0000000000−2i2i002-2000000000000000000000000000000000000
χ6944-4-44-44-4-20−4i−4i4i4i000-2222-2-22−4i4i004-400002i2i−2i−2i00000000002i−2i00-22000000000000000000000000000000000000
χ7044-4-4-44-444000000004-4-44-4-4400000000000000000000000000000000000000000022−22−222200000000000000000000
χ7144-4-4-44-444000000004-4-44-4-44000000000000000000000000000000000000000000−222222−2200000000000000000000
χ724-44-44-4-44404-4-44000-44-4-4-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ734-44-44-4-4440-444-4000-44-4-4-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ744-44-44-4-44-204-4-440002-2222-2-20000000000-222-20000000000000000−2i32i3−2i32i300000000000000000000000000000000
χ754-44-44-4-44-204-4-440002-2222-2-20000000000-222-200000000000000002i3−2i32i3−2i300000000000000000000000000000000
χ764-44-44-4-44-20-444-40002-2222-2-200000000002-2-220000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ774-44-44-4-44-20-444-40002-2222-2-200000000002-2-2200000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ784-44-4-444-4400000000-44-444-4-40000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ794-44-4-444-4400000000-44-444-4-400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ804-4-4444-4-4-244i−4i4i−4i-4-4422-2-22-22004i−4i00-22-22−2i2i−2i2i000000000000−2i2i00000000000000000000000000000000000000
χ814-4-4444-4-4-24−4i4i−4i4i-4-4422-2-22-2200−4i4i00-22-222i−2i2i−2i0000000000002i−2i00000000000000000000000000000000000000
χ824-4-4444-4-4-2-44i−4i4i−4i44-422-2-22-2200−4i4i002-22-2−2i2i−2i2i0000000000002i−2i00000000000000000000000000000000000000
χ834-4-4444-4-4-2-4−4i4i−4i4i44-422-2-22-22004i−4i002-22-22i−2i2i−2i000000000000−2i2i00000000000000000000000000000000000000
χ844-4-44-4-444440000-44-4-4-44-44-440000004-4-4400000000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-240000-44-422-22-22-2000000-222-2000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ864-4-44-4-444-240000-44-422-22-22-2000000-222-20000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ874-4-44-4-444-2-400004-4422-22-22-20000002-2-22000000004-400000000000000-22-220000000000000000000000000000
χ884-4-44-4-444-2-400004-4422-22-22-20000002-2-2200000000-44000000000000002-22-20000000000000000000000000000
χ8988-8-8-88-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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