Finite Group Databasebeta

← Group #10849266

Character table — Group #10849266

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244444412121212121212121212121212121212121244448888888844121212122244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ8111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ10111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-111-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-1-1-111
χ11111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-11-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1111111-1-111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-1-11111-1-1-1-1-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1111111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111111-111-1-111-1-1-1-111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-11111-1-111
χ172222222222222-2-2-2-2222222222-2-222-2-2-2-222220000-2-200000000-2-222-2-222-2-20000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222200002200000000-2-2-2-222-2-2220000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-200002-2000000002222-2-2-2-2220000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-20000-220000000022-2-22222-2-20000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111-1-11111111100000000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-10000-2-2−i3−i3i3i3−i3−i3i3i311-1-111-1-11100000000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-122-2-2221111-1-1-1-10000-2-2i3i3−i3−i3i3i3−i3−i311-1-111-1-11100000000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1000022−i3−i3i3i3−i3−i3i3i31111-1-111-1-100000000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1000022i3i3−i3−i3i3i3−i3−i31111-1-111-1-100000000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111122-2-2-22-1-1-1-1111111-1-1-1-111110000000000002-2-1-1110000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-2-222-221111-1-1-1-111-1-1-1-11111000000000000-2211-1-10000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111122-2-22-2-1-1-1-11111111111-1-1-1-1000000000000-2211-1-10000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2222-21111-1-1-1-1111111-1-1-1-10000000000002-2-1-1110000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100002-2−i3−i3i3i3i3i3−i3−i3-1-1-1-11111-1-100000000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100002-2i3i3−i3−i3−i3−i3i3i3-1-1-1-11111-1-100000000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222111111110000-22−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-11100000000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222111111110000-22i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-11100000000000000−i3i3i3−i30000000000
χ3722-22-2-22-222i2i−2i−2i00002-2-22-22-22i−2i002-200002i2i−2i−2i00000000000000002i−2i002-200000022−2−2−i2−i2i2i2000000000000−i2i22−2
χ3822-22-2-22-222i2i−2i−2i00002-2-22-22-22i−2i002-200002i2i−2i−2i00000000000000002i−2i002-2000000−2−222i2i2−i2−i2000000000000i2−i2−22
χ3922-22-2-22-222i2i−2i−2i00002-2-22-22-2−2i2i00-2200002i2i−2i−2i0000000000000000−2i2i00-2200000022−2−2−i2−i2i2i2000000000000i2−i2−22
χ4022-22-2-22-222i2i−2i−2i00002-2-22-22-2−2i2i00-2200002i2i−2i−2i0000000000000000−2i2i00-22000000−2−222i2i2−i2−i2000000000000−i2i22−2
χ4122-22-2-22-22−2i−2i2i2i00002-2-22-22-22i−2i00-220000−2i−2i2i2i00000000000000002i−2i00-2200000022−2−2i2i2−i2−i2000000000000−i2i2−22
χ4222-22-2-22-22−2i−2i2i2i00002-2-22-22-22i−2i00-220000−2i−2i2i2i00000000000000002i−2i00-22000000−2−222−i2−i2i2i2000000000000i2−i22−2
χ4322-22-2-22-22−2i−2i2i2i00002-2-22-22-2−2i2i002-20000−2i−2i2i2i0000000000000000−2i2i002-200000022−2−2i2i2−i2−i2000000000000i2−i22−2
χ4422-22-2-22-22−2i−2i2i2i00002-2-22-22-2−2i2i002-20000−2i−2i2i2i0000000000000000−2i2i002-2000000−2−222−i2−i2i2i2000000000000−i2i2−22
χ4522-2-22-2-2220000-22-222-22-22-2-200000022-2-20000002-20000002-22-200000000002i2i−2i−2i00002i−2i2i−2i0000000000000000
χ4622-2-22-2-2220000-22-222-22-22-2-200000022-2-20000002-20000002-22-20000000000−2i−2i2i2i0000−2i2i−2i2i0000000000000000
χ4722-2-22-2-2220000-22-222-22-22-2-200000022-2-2000000-22000000-22-2200000000002i2i−2i−2i0000−2i2i−2i2i0000000000000000
χ4822-2-22-2-2220000-22-222-22-22-2-200000022-2-2000000-22000000-22-220000000000−2i−2i2i2i00002i−2i2i−2i0000000000000000
χ492-222-2-2-2220000-2-222-2222-2-2-20000002-22-200002-200002-22-2000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ502-222-2-2-2220000-2-222-2222-2-2-20000002-22-200002-200002-22-200000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ512-222-2-2-2220000-2-222-2222-2-2-20000002-22-20000-220000-22-22000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ522-222-2-2-2220000-2-222-2222-2-2-20000002-22-20000-220000-22-2200000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ532-2-2-2-222222-22-22-2-22-2-22-2-222002-2002-2-222-22-2000000000000002-2000000002-2-2200000000000000002-2000000
χ542-2-2-2-222222-22-22-2-22-2-22-2-222002-2002-2-222-22-2000000000000002-200000000-222-20000000000000000-22000000
χ552-2-2-2-222222-22-2-222-2-2-22-2-22200-2200-222-22-22-200000000000000-22000000000000000000000000002-2002-20000
χ562-2-2-2-222222-22-2-222-2-2-22-2-22200-2200-222-22-22-200000000000000-2200000000000000000000000000-2200-220000
χ572-2-2-2-22222-22-222-2-22-2-22-2-22200-22002-2-22-22-2200000000000000-22000000002-2-220000000000000000-22000000
χ582-2-2-2-22222-22-222-2-22-2-22-2-22200-22002-2-22-22-2200000000000000-2200000000-222-200000000000000002-2000000
χ592-2-2-2-22222-22-22-222-2-2-22-2-222002-200-222-2-22-22000000000000002-2000000000000000000000000002-200-220000
χ602-2-2-2-22222-22-22-222-2-2-22-2-222002-200-222-2-22-22000000000000002-200000000000000000000000000-22002-20000
χ61444-4-44-4-440000000044-4-4-4-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ62444-4-44-4-440000000044-4-4-4-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ6344-44-4-44-4-24i4i−4i−4i0000-222-22-224i−4i004-40000−2i−2i2i2i0000000000000000−2i2i00-22000000000000000000000000000000
χ6444-44-4-44-4-24i4i−4i−4i0000-222-22-22−4i4i00-440000−2i−2i2i2i00000000000000002i−2i002-2000000000000000000000000000000
χ6544-44-4-44-4-2−4i−4i4i4i0000-222-22-224i−4i00-4400002i2i−2i−2i0000000000000000−2i2i002-2000000000000000000000000000000
χ6644-44-4-44-4-2−4i−4i4i4i0000-222-22-22−4i4i004-400002i2i−2i−2i00000000000000002i−2i00-22000000000000000000000000000000
χ6744-4-44-4-44400004-44-44-44-44-4-4000000-4-44400000000000000000000000000000000000000000000000000000000
χ6844-4-44-4-44-200004-44-4-22-22-22200000022-2-200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ6944-4-44-4-44-200004-44-4-22-22-22200000022-2-2000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ7044-4-44-4-44-20000-44-44-22-22-222000000-2-2220000004-4000000-22-2200000000000000000000000000000000000000
χ7144-4-44-4-44-20000-44-44-22-22-222000000-2-222000000-440000002-22-200000000000000000000000000000000000000
χ724-444-4-4-444000044-4-4-4444-4-4-4000000-44-4400000000000000000000000000000000000000000000000000000000
χ734-444-4-4-44-2000044-4-42-2-2-22220000002-22-20000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ744-444-4-4-44-2000044-4-42-2-2-22220000002-22-200000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ754-444-4-4-44-20000-4-4442-2-2-2222000000-22-2200004-40000-22-22000000000000000000000000000000000000000000
χ764-444-4-4-44-20000-4-4442-2-2-2222000000-22-220000-4400002-22-2000000000000000000000000000000000000000000
χ774-44-44-44-444i−4i−4i4i0000-44-4-444-400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ784-44-44-44-44−4i4i4i−4i0000-44-4-444-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ794-44-44-44-4-24i−4i−4i4i00002-222-2-220000000000−2i2i2i−2i000000000000000000−2i32i30023−230000000000000000000000000000
χ804-44-44-44-4-24i−4i−4i4i00002-222-2-220000000000−2i2i2i−2i0000000000000000002i3−2i300−23230000000000000000000000000000
χ814-44-44-44-4-2−4i4i4i−4i00002-222-2-2200000000002i−2i−2i2i000000000000000000−2i32i300−23230000000000000000000000000000
χ824-44-44-44-4-2−4i4i4i−4i00002-222-2-2200000000002i−2i−2i2i0000000000000000002i3−2i30023−230000000000000000000000000000
χ834-4-4444-4-4400000000-4-4-444-44000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ844-4-4444-4-4400000000-4-4-444-440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ854-4-4-4-4444-24-44-44-4-4422-222-2-2004-400-222-2-22-2200000000000000-22000000000000000000000000000000000000
χ864-4-4-4-4444-24-44-4-444-422-222-2-200-44002-2-22-22-22000000000000002-2000000000000000000000000000000000000
χ874-4-4-4-4444-2-44-444-4-4422-222-2-200-4400-222-22-22-2000000000000002-2000000000000000000000000000000000000
χ884-4-4-4-4444-2-44-44-444-422-222-2-2004-4002-2-222-22-200000000000000-22000000000000000000000000000000000000
χ89888-8-88-8-8-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000

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