Finite Group Databasebeta

← Group #10845925

Character table — Group #10845925

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444466666666666688888888888888881212121212121212121216161616161616161616242424244848
order1222222234444666666622448888888812121212444488888888444466121224242424242424242244448888441212121212121212444444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1111-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1-1-11
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-111-1-1-11
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1111-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-111-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1111-1-1-1-11111-1-11-1
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-1-1-11111-1-1-1-111-11
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
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000000022-2-2-1-1-1-11111111100000000002-2-1-1-1-11111000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1000000000000-2-222-1-1-1-1111111110000000000-221111-1-1-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-100000000000022221111-1-1-1-111110000000000-2-2-1-111-1-111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000000000-2-2-2-21111-1-1-1-1111100000000002211-1-111-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-100000000000022-2-211111111-1-1-1-10000000000-22-1-11111-1-1000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000-2-22211111111-1-1-1-100000000002-211-1-1-1-111000000
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
χ332222-2-2-2-220000222-2-2-2-2-220022−2−2−2−222000022-2-22222−2−2−2−20000-220022−2−2−2−222-220000−2−2220000000000000000
χ342222-2-2-2-220000222-2-2-2-2-220022−2−2−2−2220000-2-222−2−2−2−222220000-220022−2−2−2−2222-2000022−2−20000000000000000
χ352222-2-2-2-220000222-2-2-2-2-2200−2−22222−2−2000022-2-2−2−2−2−222220000-2200−2−22222−2−2-22000022−2−20000000000000000
χ362222-2-2-2-220000222-2-2-2-2-2200−2−22222−2−20000-2-2222222−2−2−2−20000-2200−2−22222−2−22-20000−2−2220000000000000000
χ3722-2-2-22-2222-22-22-2-22-22-20000000000002-22-200002i2i−2i−2i2i2i−2i−2i2i−2i000000000000000000000000002i−2i0000002-20000
χ3822-2-2-22-2222-22-22-2-22-22-20000000000002-22-200002i2i−2i−2i2i2i−2i−2i−2i2i00000000000000000000000000−2i2i000000-220000
χ3922-2-2-22-2222-22-22-2-22-22-20000000000002-22-20000−2i−2i2i2i−2i−2i2i2i2i−2i000000000000000000000000002i−2i000000-220000
χ4022-2-2-22-2222-22-22-2-22-22-20000000000002-22-20000−2i−2i2i2i−2i−2i2i2i−2i2i00000000000000000000000000−2i2i0000002-20000
χ412-22-2-2-22222-2-22-22-2-2-2220000000000002-2-2200002-22-22-22-2002-200000000000000000000000000002-200002-200
χ422-22-2-2-22222-2-22-22-2-2-2220000000000002-2-2200002-22-22-22-200-220000000000000000000000000000-220000-2200
χ432-22-2-2-22222-2-22-22-2-2-2220000000000002-2-220000-22-22-22-22002-200000000000000000000000000002-20000-2200
χ442-22-2-2-22222-2-22-22-2-2-2220000000000002-2-220000-22-22-22-2200-220000000000000000000000000000-2200002-200
χ452-2-222-2-22222-2-2-2-22-222-200002i−2i2i−2i000022-2-22-22-22i−2i−2i2i2i−2i−2i2i000000002i−2i2i−2i0000002-20000000000000000000000
χ462-2-222-2-22222-2-2-2-22-222-200002i−2i2i−2i000022-2-2-22-22−2i2i2i−2i−2i2i2i−2i000000002i−2i2i−2i000000-220000000000000000000000
χ472-2-222-2-22222-2-2-2-22-222-20000−2i2i−2i2i000022-2-22-22-2−2i2i2i−2i−2i2i2i−2i00000000−2i2i−2i2i0000002-20000000000000000000000
χ482-2-222-2-22222-2-2-2-22-222-20000−2i2i−2i2i000022-2-2-22-222i−2i−2i2i2i−2i−2i2i00000000−2i2i−2i2i000000-220000000000000000000000
χ492-2-222-2-222-2-222-2-22-222-2000000002-22-2-2-2222-22-2000000000000000000002-22-200-22002-22-20000000000000000
χ502-2-222-2-222-2-222-2-22-222-2000000002-22-2-2-222-22-22000000000000000000002-22-2002-200-22-220000000000000000
χ512-2-222-2-222-2-222-2-22-222-200000000-22-22-2-2222-22-200000000000000000000-22-2200-2200-22-220000000000000000
χ522-2-222-2-222-2-222-2-22-222-200000000-22-22-2-222-22-2200000000000000000000-22-22002-2002-22-20000000000000000
χ532-2-22-222-220000-2-222-2-22002i−2i−i2i2i2−i22−2−2200002-2-22−i2i2i2−i2i2−i2−i2i20000002i−2i−i2i2i2−i22−2−2200002i−2i2−2−220000000000000000
χ542-2-22-222-220000-2-222-2-22002i−2i−i2i2i2−i22−2−220000-222-2i2−i2−i2i2−i2i2i2−i20000002i−2i−i2i2i2−i22−2−220000−2i2i−222−20000000000000000
χ552-2-22-222-220000-2-222-2-22002i−2ii2−i2−i2i2−222−200002-2-22i2−i2−i2i2−i2i2i2−i20000002i−2ii2−i2−i2i2−222−200002i−2i−222−20000000000000000
χ562-2-22-222-220000-2-222-2-22002i−2ii2−i2−i2i2−222−20000-222-2−i2i2i2−i2i2−i2−i2i20000002i−2ii2−i2−i2i2−222−20000−2i2i2−2−220000000000000000
χ572-2-22-222-220000-2-222-2-2200−2i2i−i2i2i2−i2−222−200002-2-22−i2i2i2−i2i2−i2−i2i2000000−2i2i−i2i2i2−i2−222−20000−2i2i−222−20000000000000000
χ582-2-22-222-220000-2-222-2-2200−2i2i−i2i2i2−i2−222−20000-222-2i2−i2−i2i2−i2i2i2−i2000000−2i2i−i2i2i2−i2−222−200002i−2i2−2−220000000000000000
χ592-2-22-222-220000-2-222-2-2200−2i2ii2−i2−i2i22−2−2200002-2-22i2−i2−i2i2−i2i2i2−i2000000−2i2ii2−i2−i2i22−2−220000−2i2i2−2−220000000000000000
χ602-2-22-222-220000-2-222-2-2200−2i2ii2−i2−i2i22−2−220000-222-2−i2i2i2−i2i2−i2−i2i2000000−2i2ii2−i2−i2i22−2−2200002i−2i−222−20000000000000000
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
χ6744-4-44-44-4400004-4-4-44-4400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000000000
χ6844-4-44-44-4400004-4-4-44-44000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6944-4-4-44-444-44-444-4-44-44-4000000000000-44-44000000000000000000000000000000000000000000000000000000
χ7044-4-4-44-44-24-44-4-222-22-22000000000000-22-220000000000004i−4i00000000000000000000000000−2i2i000000000000
χ7144-4-4-44-44-24-44-4-222-22-22000000000000-22-22000000000000−4i4i000000000000000000000000002i−2i000000000000
χ7244-4-4-44-44-2-44-44-222-22-220000000000002-22-200000000000000000000000000000000000000000023−230000000000
χ7344-4-4-44-44-2-44-44-222-22-220000000000002-22-2000000000000000000000000000000000000000000−23230000000000
χ744-44-444-4-440000-44-444-4-40000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000000000
χ754-44-444-4-440000-44-444-4-400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000000000
χ764-44-4-4-4444-444-4-44-4-4-444000000000000-444-4000000000000000000000000000000000000000000000000000000
χ774-44-4-4-444-24-4-442-2222-2-2000000000000-222-2000000000000004-40000000000000000000000000000-2200000000
χ784-44-4-4-444-24-4-442-2222-2-2000000000000-222-200000000000000-4400000000000000000000000000002-200000000
χ794-44-4-4-444-2-444-42-2222-2-20000000000002-2-220000000000000000000000000000000000000000000000−2i32i3000000
χ804-44-4-4-444-2-444-42-2222-2-20000000000002-2-2200000000000000000000000000000000000000000000002i3−2i3000000
χ814-4-444-4-44-244-4-422-22-2-2200004i−4i4i−4i0000-2-22200000000000000000000−2i2i−2i2i000000000000000000000000000000
χ824-4-444-4-44-244-4-422-22-2-220000−4i4i−4i4i0000-2-222000000000000000000002i−2i2i−2i000000000000000000000000000000
χ834-4-444-4-44-2-4-44422-22-2-22000000004-44-422-2-2000000000000000000000000-22-2200000000000000000000000000
χ844-4-444-4-44-2-4-44422-22-2-2200000000-44-4422-2-20000000000000000000000002-22-200000000000000000000000000
χ854-4-44-444-4-2000022-2-222-2004i−4i−2i22i22i2−2i222−22−22220000000000000000000000−2i2ii2−i2−i2i2−222−200000000000000000000000000
χ864-4-44-444-4-2000022-2-222-2004i−4i2i2−2i2−2i22i2−222222−220000000000000000000000−2i2i−i2i2i2−i22−2−2200000000000000000000000000
χ874-4-44-444-4-2000022-2-222-200−4i4i−2i22i22i2−2i2−222222−2200000000000000000000002i−2ii2−i2−i2i22−2−2200000000000000000000000000
χ884-4-44-444-4-2000022-2-222-200−4i4i2i2−2i2−2i22i222−22−222200000000000000000000002i−2i−i2i2i2−i2−222−200000000000000000000000000
χ8988-8-88-88-8-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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