Finite Group Databasebeta

← Group #10848596

Character table — Group #10848596

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666666644444444441212121212121212121212121212121212121212121212121212121244444444441212121212121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11111-11111-1-1
χ91111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111111-111-1-111-1-1-111-1-1-111-1-11-1
χ101111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-111-1-111-1-11-1-1111-1-111-11
χ111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111111-11-1-111-1-111-1-1-111-111-1-1-11
χ121111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-1-111111-1-11-1-1111-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1111-1-1-1-111-111-1-1-1-1-111-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1111-1-1-1-1111-1-111111-1-11-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111-1-1-11111-1-1-1-1-111-1-1-1111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-1-1-11111-1-1111-1-1111-1-1-11
χ17222222222-2-2-2-2-2-222222222-2000000002222-2-2-2-20000000000000000-2-2-2-22-22-20000002-22-20000000000000000
χ18222222222-2-2-2-2-2-222222222-2000000002222-2-2-2-20000000000000000-2-2-2-2-22-22000000-22-220000000000000000
χ192222222-2-222-2-2-2-22222222-2200000000-2-2-2-222220000000000000000-2-2-2-22-2-220000002-2-220000000000000000
χ202222222-2-222-2-2-2-22222222-2200000000-2-2-2-222220000000000000000-2-2-2-2-222-2000000-222-20000000000000000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-1-1-1-122220000-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-2-2-2-20000221111-1-1-1-1000000000000
χ25222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i311112-22-2000000-11-11−i3i3−i3i3000000000000
χ26222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i31111-22-220000001-11-1i3−i3i3−i3000000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i311112-22-2000000-11-11i3−i3i3−i3000000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i31111-22-220000001-11-1−i3i3−i3i3000000000000
χ29222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i311112-2-22000000-111-1−i3i3i3−i3000000000000
χ30222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-222-20000001-1-11i3−i3−i3i3000000000000
χ31222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i311112-2-22000000-111-1i3−i3−i3i3000000000000
χ32222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-222-20000001-1-11−i3i3i3−i3000000000000
χ33222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-122-2-200002-2-1-111-1-111000000000000
χ34222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2220000-2211-1-111-1-1000000000000
χ35222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ36222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ372222-2-222222-222-222-2-2-2-22-2-20000000022-2-222-2-2000000000000000022-2-200000000000000000002-22-20000000
χ382222-2-222222-222-222-2-2-2-22-2-20000000022-2-222-2-2000000000000000022-2-20000000000000000000-22-220000000
χ392222-2-2222-2-22-2-2222-2-2-2-22-220000000022-2-2-2-2220000000000000000-2-222000022-2-2000000000020000-2000000
χ402222-2-2222-2-22-2-2222-2-2-2-22-220000000022-2-2-2-2220000000000000000-2-2220000-2-2220000000000-200002000000
χ412222-2-22-2-2222-2-2222-2-2-2-222-200000000-2-22222-2-20000000000000000-2-222000022-2-20000000000-200002000000
χ422222-2-22-2-2222-2-2222-2-2-2-222-200000000-2-22222-2-20000000000000000-2-2220000-2-222000000000020000-2000000
χ432222-2-22-2-2-2-2-222-222-2-2-2-222200000000-2-222-2-222000000000000000022-2-200000000000000000002-2-220000000
χ442222-2-22-2-2-2-2-222-222-2-2-2-222200000000-2-222-2-222000000000000000022-2-20000000000000000000-222-20000000
χ452-2-222-22000022-2-2-2-222-2-2200000022-2-2000000000000000022-2-222-2-22-22-200002i−2i2i−2i0000000000000000002i−2i00
χ462-2-222-22000022-2-2-2-222-2-2200000022-2-2000000000000000022-2-222-2-22-22-20000−2i2i−2i2i000000000000000000−2i2i00
χ472-2-222-22000022-2-2-2-222-2-22000000-2-2220000000000000000-2-222-2-2222-22-200002i−2i2i−2i000000000000000000−2i2i00
χ482-2-222-22000022-2-2-2-222-2-22000000-2-2220000000000000000-2-222-2-2222-22-20000−2i2i−2i2i0000000000000000002i−2i00
χ492-2-22-22200002-22-2-2-2-2-22220022-2-200000000000022-2-222-2-200000000-222-200002i−2i−2i2i00000000000000002i−2i0000
χ502-2-22-22200002-22-2-2-2-2-22220022-2-200000000000022-2-222-2-200000000-222-20000−2i2i2i−2i0000000000000000−2i2i0000
χ512-2-22-22200002-22-2-2-2-2-222200-2-222000000000000-2-222-2-22200000000-222-200002i−2i−2i2i0000000000000000−2i2i0000
χ522-2-22-22200002-22-2-2-2-2-222200-2-222000000000000-2-222-2-22200000000-222-20000−2i2i2i−2i00000000000000002i−2i0000
χ534444-4-4-24444-444-4-2-22222-2-4-400000000-2-222-2-2220000000000000000-2-222000000000000000000000000000000
χ544444-4-4-244-4-44-4-44-2-22222-2-4400000000-2-22222-2-2000000000000000022-2-2000000000000000000000000000000
χ554444-4-4-2-4-4444-4-44-2-22222-24-40000000022-2-2-2-222000000000000000022-2-2000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-444-4-2-22222-2440000000022-2-222-2-20000000000000000-2-222000000000000000000000000000000
χ5744-4-4004004-400004-40000-4002-22-22-22-200004-4002-22-22-22-22-22-22-22-20000000000000000000000000000000000
χ5844-4-4004004-400004-40000-400-22-22-22-2200004-400-22-22-22-22-22-22-22-220000000000000000000000000000000000
χ5944-4-400400-4400004-40000-4002-22-2-22-220000-44002-22-22-22-2-22-22-22-220000000000000000000000000000000000
χ6044-4-400400-4400004-40000-400-22-222-22-20000-4400-22-22-22-222-22-22-22-20000000000000000000000000000000000
χ6144-4-400-2004-40000-22−2i32i3−2i32i32002-22-22-22-20000-22−2i32i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000000000000000
χ6244-4-400-2004-40000-22−2i32i3−2i32i3200-22-22-22-220000-22−2i32i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000000000000000
χ6344-4-400-2004-40000-222i3−2i32i3−2i32002-22-22-22-20000-222i3−2i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000000000000000
χ6444-4-400-2004-40000-222i3−2i32i3−2i3200-22-22-22-220000-222i3−2i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000000000000000
χ6544-4-400-200-440000-22−2i32i3−2i32i32002-22-2-22-2200002-22i3−2i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000000000000000
χ6644-4-400-200-440000-22−2i32i3−2i32i3200-22-222-22-200002-22i3−2i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000000000000000
χ6744-4-400-200-440000-222i3−2i32i3−2i32002-22-2-22-2200002-2−2i32i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000000000000000
χ6844-4-400-200-440000-222i3−2i32i3−2i3200-22-222-22-200002-2−2i32i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000000000000000
χ694-44-40044-4000000-440000-4002-2-222-2-224-40000002-2-222-2-222-2-222-2-220000000000000000000000000000000000
χ704-44-40044-4000000-440000-400-222-2-222-24-4000000-222-2-222-2-222-2-222-20000000000000000000000000000000000
χ714-44-4004-44000000-440000-4002-2-22-222-2-440000002-2-222-2-22-222-2-222-20000000000000000000000000000000000
χ724-44-4004-44000000-440000-400-222-22-2-22-44000000-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ734-44-400-24-40000002-2−2i32i32i3−2i32002-2-222-2-22-22−2i32i30000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ744-44-400-24-40000002-2−2i32i32i3−2i3200-222-2-222-2-22−2i32i300001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ754-44-400-24-40000002-22i3−2i3−2i32i32002-2-222-2-22-222i3−2i30000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ764-44-400-24-40000002-22i3−2i3−2i32i3200-222-2-222-2-222i3−2i300001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ774-44-400-2-440000002-2−2i32i32i3−2i32002-2-22-222-22-22i3−2i30000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ784-44-400-2-440000002-2−2i32i32i3−2i3200-222-22-2-222-22i3−2i300001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ794-44-400-2-440000002-22i3−2i3−2i32i32002-2-22-222-22-2−2i32i30000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ804-44-400-2-440000002-22i3−2i3−2i32i3200-222-22-2-222-2−2i32i300001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ814-4-444-440000-4-444-4-444-4-440000000000000000000000000000000000-44-44000000000000000000000000000000
χ824-4-444-4-2000044-4-422-2-222-200000044-4-40000000000000000-2-222-2-222-22-22000000000000000000000000000000
χ834-4-444-4-2000044-4-422-2-222-2000000-4-444000000000000000022-2-222-2-2-22-22000000000000000000000000000000
χ844-4-444-4-20000-4-44422-2-222-200000000000000000000000000−2i3−2i32i32i32i32i3−2i3−2i32-22-2000000000000000000000000000000
χ854-4-444-4-20000-4-44422-2-222-2000000000000000000000000002i32i3−2i3−2i3−2i3−2i32i32i32-22-2000000000000000000000000000000
χ864-4-44-4440000-44-44-4-4-4-444400000000000000000000000000000000004-4-44000000000000000000000000000000
χ874-4-44-44-200004-44-42222-2-2-20044-4-4000000000000-2-222-2-222000000002-2-22000000000000000000000000000000
χ884-4-44-44-200004-44-42222-2-2-200-4-44400000000000022-2-222-2-2000000002-2-22000000000000000000000000000000
χ894-4-44-44-20000-44-442222-2-2-2000000000000000000−2i3−2i32i32i32i32i3−2i3−2i300000000-222-2000000000000000000000000000000
χ904-4-44-44-20000-44-442222-2-2-20000000000000000002i32i3−2i3−2i3−2i3−2i32i32i300000000-222-2000000000000000000000000000000

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