Finite Group Databasebeta

← Group #10877424

Character table — Group #10877424

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444466666666666688888888888888881212121212121212121216161616161616161616242424244848
order122222223444466666664444888888881212121222228888888844441212121224242424242424244444448888441212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-111-1-11-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111-1-1-11111-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111-1111-1-1-1-111-1-1111-1
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11-1-1-11111-1-1-1-1111-1
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1111-1-1-1-11111-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111111-1-111-1-111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1111111-1-1
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-2222200000000000022-2-20000000022-2-2-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-2-2-200000000000022-2-200000000-2-2222200000000000000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-22222000000000000-2-22200000000-2-2-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-2-2-2000000000000-2-222000000002222-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-10000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-1-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1000000000000-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-211111111000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000000022-2-2-1-1-1-1111111110000000000-221111-1-1-1-1000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1000000000000-2-222-1-1-1-11111111100000000002-2-1-1-1-11111000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-100000000000022-2-21111-1-1-1-1111100000000002-211-1-1-1-111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000000000-2-2221111-1-1-1-111110000000000-22-1-11111-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000222211111111-1-1-1-10000000000-2-2-1-111-1-111000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000-2-2-2-211111111-1-1-1-100000000002211-1-111-1-1000000
χ292222-2-2-2-220000222-2-2-2-22-20022−2−222−2−2000022-2-22222−2−2−2−200002-20022−2−222−2−22-2000022−2−20000000000000000
χ302222-2-2-2-220000222-2-2-2-22-20022−2−222−2−20000-2-222−2−2−2−2222200002-20022−2−222−2−2-220000−2−2220000000000000000
χ312222-2-2-2-220000222-2-2-2-22-200−2−222−2−222000022-2-2−2−2−2−2222200002-200−2−222−2−2222-20000−2−2220000000000000000
χ322222-2-2-2-220000222-2-2-2-22-200−2−222−2−2220000-2-2222222−2−2−2−200002-200−2−222−2−222-22000022−2−20000000000000000
χ332222-2-2-2-220000222-2-2-2-2-220022−2−2−2−222000022-2-2−2−2−2−222220000-220022−2−2−2−222-22000022−2−20000000000000000
χ342222-2-2-2-220000222-2-2-2-2-220022−2−2−2−2220000-2-2222222−2−2−2−20000-220022−2−2−2−2222-20000−2−2220000000000000000
χ352222-2-2-2-220000222-2-2-2-2-2200−2−22222−2−2000022-2-22222−2−2−2−20000-2200−2−22222−2−2-220000−2−2220000000000000000
χ362222-2-2-2-220000222-2-2-2-2-2200−2−22222−2−20000-2-222−2−2−2−222220000-2200−2−22222−2−22-2000022−2−20000000000000000
χ3722-2-22-2-22200002-2-2-222-2002-2−i2i2−i2i2−i2i2−i2i200002-22-2−i2−i2i2i2−i2−i2i2i20000002-2−i2i2−i2i2−i2i2−i2i200002-2−i2i2−i2i20000000000000000
χ3822-2-22-2-22200002-2-2-222-2002-2−i2i2−i2i2−i2i2−i2i20000-22-22i2i2−i2−i2i2i2−i2−i20000002-2−i2i2−i2i2−i2i2−i2i20000-22i2−i2i2−i20000000000000000
χ3922-2-22-2-22200002-2-2-222-2002-2i2−i2i2−i2i2−i2i2−i200002-22-2i2i2−i2−i2i2i2−i2−i20000002-2i2−i2i2−i2i2−i2i2−i200002-2i2−i2i2−i20000000000000000
χ4022-2-22-2-22200002-2-2-222-2002-2i2−i2i2−i2i2−i2i2−i20000-22-22−i2−i2i2i2−i2−i2i2i20000002-2i2−i2i2−i2i2−i2i2−i20000-22−i2i2−i2i20000000000000000
χ4122-2-22-2-22200002-2-2-222-200-22−i2i2−i2i2i2−i2i2−i200002-22-2i2i2−i2−i2i2i2−i2−i2000000-22−i2i2−i2i2i2−i2i2−i20000-22−i2i2−i2i20000000000000000
χ4222-2-22-2-22200002-2-2-222-200-22−i2i2−i2i2i2−i2i2−i20000-22-22−i2−i2i2i2−i2−i2i2i2000000-22−i2i2−i2i2i2−i2i2−i200002-2i2−i2i2−i20000000000000000
χ4322-2-22-2-22200002-2-2-222-200-22i2−i2i2−i2−i2i2−i2i200002-22-2−i2−i2i2i2−i2−i2i2i2000000-22i2−i2i2−i2−i2i2−i2i20000-22i2−i2i2−i20000000000000000
χ4422-2-22-2-22200002-2-2-222-200-22i2−i2i2−i2−i2i2−i2i20000-22-22i2i2−i2−i2i2i2−i2−i2000000-22i2−i2i2−i2−i2i2−i2i200002-2−i2i2−i2i20000000000000000
χ4522-2-2-222-222-2-222-2-22-2-2200002i−2i−2i2i00002-22-22-2-2200000000000000002i−2i−2i2i0000002-2002i−2i−2i2i0000000000000000
χ4622-2-2-222-222-2-222-2-22-2-2200002i−2i−2i2i00002-22-2-222-200000000000000002i−2i−2i2i000000-2200−2i2i2i−2i0000000000000000
χ4722-2-2-222-222-2-222-2-22-2-220000−2i2i2i−2i00002-22-22-2-220000000000000000−2i2i2i−2i0000002-200−2i2i2i−2i0000000000000000
χ4822-2-2-222-222-2-222-2-22-2-220000−2i2i2i−2i00002-22-2-222-20000000000000000−2i2i2i−2i000000-22002i−2i−2i2i0000000000000000
χ4922-2-2-222-22-222-22-2-22-2-22000000002i−2i−2i2i-22-222-2-222i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i00-220000000000000000000000
χ5022-2-2-222-22-222-22-2-22-2-22000000002i−2i−2i2i-22-22-222-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i002-20000000000000000000000
χ5122-2-2-222-22-222-22-2-22-2-2200000000−2i2i2i−2i-22-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i00-220000000000000000000000
χ5222-2-2-222-22-222-22-2-22-2-2200000000−2i2i2i−2i-22-22-222-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i002-20000000000000000000000
χ532-22-222-2-22-2-222-2-222-22-2000000000000-222-200002-22-22-22-22i−2i0000000000000000000000000000002i−2i00002i−2i00
χ542-22-222-2-22-2-222-2-222-22-2000000000000-222-200002-22-22-22-2−2i2i000000000000000000000000000000−2i2i0000−2i2i00
χ552-22-222-2-22-2-222-2-222-22-2000000000000-222-20000-22-22-22-222i−2i0000000000000000000000000000002i−2i0000−2i2i00
χ562-22-222-2-22-2-222-2-222-22-2000000000000-222-20000-22-22-22-22−2i2i000000000000000000000000000000−2i2i00002i−2i00
χ572-2-22-22-2222-22-2-22-222-2-200000000000022-2-200002i−2i−2i2i−2i2i2i−2i002-20000000000000000000000002-20000002i−2i0000
χ582-2-22-22-2222-22-2-22-222-2-200000000000022-2-200002i−2i−2i2i−2i2i2i−2i00-22000000000000000000000000-22000000−2i2i0000
χ592-2-22-22-2222-22-2-22-222-2-200000000000022-2-20000−2i2i2i−2i2i−2i−2i2i002-20000000000000000000000002-2000000−2i2i0000
χ602-2-22-22-2222-22-2-22-222-2-200000000000022-2-20000−2i2i2i−2i2i−2i−2i2i00-22000000000000000000000000-220000002i−2i0000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000000022220000000000000000-2-2220000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000000002222000000000000000022-2-20000000000000000000000000000000000
χ634444-4-4-4-4-20000-2-2-222224-4002222−22−222222−22−2200000000000000000000-2200−2−222−2−22200000000000000000000000000
χ644444-4-4-4-4-20000-2-2-222224-400−22−222222−22−22222200000000000000000000-220022−2−222−2−200000000000000000000000000
χ654444-4-4-4-4-20000-2-2-22222-44002222−22−22−22−222222000000000000000000002-200−2−22222−2−200000000000000000000000000
χ664444-4-4-4-4-20000-2-2-22222-4400−22−2222222222−22−22000000000000000000002-20022−2−2−2−22200000000000000000000000000
χ6744-4-44-4-44-20000-2222-2-22004-4−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000-22i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ6844-4-44-4-44-20000-2222-2-22004-42i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000-22−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6944-4-44-4-44-20000-2222-2-2200-44−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002-2i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ7044-4-44-4-44-20000-2222-2-2200-442i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000002-2−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ7144-4-4-444-4-24-4-44-222-222-200004i−4i−4i4i0000-22-2200000000000000000000−2i2i2i−2i000000000000000000000000000000
χ7244-4-4-444-4-24-4-44-222-222-20000−4i4i4i−4i0000-22-22000000000000000000002i−2i−2i2i000000000000000000000000000000
χ7344-4-4-444-4-2-444-4-222-222-2000000004i−4i−4i4i2-22-2000000000000000000000000−2i2i2i−2i00000000000000000000000000
χ7444-4-4-444-4-2-444-4-222-222-200000000−4i4i4i−4i2-22-20000000000000000000000002i−2i−2i2i00000000000000000000000000
χ754-44-444-4-4444-4-4-4-444-44-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ764-44-444-4-4-244-4-422-2-22-22000000000000-222-2000000000000000000000000000000000000000000000023−23000000
χ774-44-444-4-4-244-4-422-2-22-22000000000000-222-20000000000000000000000000000000000000000000000−2323000000
χ784-44-444-4-4-2-4-44422-2-22-220000000000002-2-220000000000004i−4i000000000000000000000000000000−2i2i00000000
χ794-44-444-4-4-2-4-44422-2-22-220000000000002-2-22000000000000−4i4i0000000000000000000000000000002i−2i00000000
χ804-44-4-4-44440000-4-44-44-440000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000000000
χ814-44-4-4-44440000-4-44-44-4400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000000000
χ824-4-444-44-440000-44-4-4-44400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ834-4-444-44-440000-44-4-4-444000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ844-4-44-44-444-44-44-44-444-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000
χ854-4-44-44-44-24-44-42-22-2-222000000000000-2-222000000000000004-4000000000000000000000000-22000000000000
χ864-4-44-44-44-24-44-42-22-2-222000000000000-2-22200000000000000-440000000000000000000000002-2000000000000
χ874-4-44-44-44-2-44-442-22-2-22200000000000022-2-200000000000000000000000000000000000000000023−230000000000
χ884-4-44-44-44-2-44-442-22-2-22200000000000022-2-2000000000000000000000000000000000000000000−23230000000000
χ898-88-8-8-888-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-88-8-400004-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000

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