Finite Group Databasebeta

← Group #10849301

Character table — Group #10849301

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666664444444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-111-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-111-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-1111-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-111-1-11111-1-1-1-11111-1-11111-1-111-1-1-11
χ1311111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-11
χ1411111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-22222222222222-2-2000022222222222200000000-2-2-2-2000000-2-2-2-2-2-2-2-200000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-200000000-2-2-2-200000022-2-2222200000000000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2220000-2-2-2-22222-2-2-2-200000000-2-2-2-2000000-2222-2-22200000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222220000-2-2-2-2-2-2-2-2222200000000-2-2-2-20000002-22222-2-200000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2-2-222-1-1-1-1-1-111111111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-11111-1-1-1-11111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-2-22222-2-2-1-111111111-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22-211-1-1111111-1-1-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-21111-1-1-1-1111111111111-1-1-1-122-2-2222-211-1-111-1-1-1-11111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-221111-1-111111111-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-211111111-1-1-1-111111111-1-1-1-12222-2-2-221111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-20000-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i31111000000-2-2111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1222222-2-20000-1-1-1-1-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i31111000000-2-2111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-111111111−i3−i3−i3−i3i3i3i3i311110000002211-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-111111111i3i3i3i3−i3−i3−i3−i311110000002211-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22200001111-1-1-1-11111−i3−i3−i3−i3i3i3i3i31111000000-22-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22200001111-1-1-1-11111i3i3i3i3−i3−i3−i3−i31111000000-22-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i311110000002-2-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i311110000002-2-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3722-22-22-2-22-22-2222-2-2-2-22000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i22-2-200000000000000000000000000002-2002i−2i000000
χ3822-22-22-2-22-22-2222-2-2-2-22000000002i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000-2200−2i2i000000
χ3922-22-22-2-22-22-2222-2-2-2-2200000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i22-2-200000000000000000000000000002-200−2i2i000000
χ4022-22-22-2-22-22-2222-2-2-2-2200000000−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i22-2-20000000000000000000000000000-22002i−2i000000
χ412-22-222-2-22-2-222-2-222-2-22000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000002-2002i−2i00000000
χ422-22-222-2-22-2-222-2-222-2-22000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000-2200−2i2i00000000
χ432-22-222-2-22-2-222-2-222-2-2200000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000002-200−2i2i00000000
χ442-22-222-2-22-2-222-2-222-2-2200000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000-22002i−2i00000000
χ452-2-2-2-222222-2-22-2-2-2-22222-200002-22-2-2222-2-2000000002-2-222-2-222-2-222-20000002-200002-22-20000000000000000000000
χ462-2-2-2-222222-2-22-2-2-2-22222-200002-2-222-222-2-200000000-222-2-222-22-2-22-220000002-20000-22-220000000000000000000000
χ472-2-2-2-222222-2-22-2-2-2-2222-220000-222-2-22-2-222000000002-2-222-2-222-2-22-22000000-220000-22-220000000000000000000000
χ482-2-2-2-222222-2-22-2-2-2-2222-220000-22-222-2-2-22200000000-222-2-222-22-2-222-2000000-2200002-22-20000000000000000000000
χ492-2-2-2-22222-222-2-2-2-2-22222-20000-22000022-2-20000000000000000-222-2002-22-200-22000000002-22-22-22-200000000000000
χ502-2-2-2-22222-222-2-2-2-2-22222-20000-22000022-2-20000000000000000-222-200-22-2200-2200000000-22-22-22-2200000000000000
χ512-2-2-2-22222-222-2-2-2-2-2222-2200002-20000-2-2220000000000000000-222-2002-2-22002-2000000002-22-2-22-2200000000000000
χ522-2-2-2-22222-222-2-2-2-2-2222-2200002-20000-2-2220000000000000000-222-200-222-2002-200000000-22-222-22-200000000000000
χ532-2-2-2-2222-12-2-221111-1-1-12-200002-22-2-22-1-111−i3−i3i3i3−i3−i3i3i3-111-1-111-1-111-12-2000000-11−i3i3−i3i3-11-11−i3i3i3−i3−i3i3i3−i300000000000000
χ542-2-2-2-2222-12-2-221111-1-1-12-200002-22-2-22-1-111i3i3−i3−i3i3i3−i3−i3-111-1-111-1-111-12-2000000-11i3−i3i3−i3-11-11i3−i3−i3i3i3−i3−i3i300000000000000
χ552-2-2-2-2222-12-2-221111-1-1-12-200002-2-222-2-1-111−i3−i3i3i3−i3−i3i3i31-1-111-1-11-111-1-22000000-11−i3i3−i3i31-11-1i3−i3−i3i3i3−i3−i3i300000000000000
χ562-2-2-2-2222-12-2-221111-1-1-12-200002-2-222-2-1-111i3i3−i3−i3i3i3−i3−i31-1-111-1-11-111-1-22000000-11i3−i3i3−i31-11-1−i3i3i3−i3−i3i3i3−i300000000000000
χ572-2-2-2-2222-12-2-221111-1-1-1-220000-222-2-2211-1-1−i3−i3i3i3i3i3−i3−i3-111-1-111-1-111-1-220000001-1−i3i3i3−i31-11-1−i3i3i3−i3i3−i3−i3i300000000000000
χ582-2-2-2-2222-12-2-221111-1-1-1-220000-222-2-2211-1-1i3i3−i3−i3−i3−i3i3i3-111-1-111-1-111-1-220000001-1i3−i3−i3i31-11-1i3−i3−i3i3−i3i3i3−i300000000000000
χ592-2-2-2-2222-12-2-221111-1-1-1-220000-22-222-211-1-1−i3−i3i3i3i3i3−i3−i31-1-111-1-11-111-12-20000001-1−i3i3i3−i3-11-11i3−i3−i3i3−i3i3i3−i300000000000000
χ602-2-2-2-2222-12-2-221111-1-1-1-220000-22-222-211-1-1i3i3−i3−i3−i3−i3i3i31-1-111-1-11-111-12-20000001-1i3−i3−i3i3-11-11−i3i3i3−i3i3−i3−i3i300000000000000
χ612-2-2-2-2222-1-222-21111-1-1-12-20000-220000-1-111−i3−i3i3i3−i3−i3i3i3−i3i3i3−i3i3−i3−i3i31-1-11002-22-2001-1i3−i3i3−i3−i3i3i3−i3-11-11-11-1100000000000000
χ622-2-2-2-2222-1-222-21111-1-1-12-20000-220000-1-111−i3−i3i3i3−i3−i3i3i3i3−i3−i3i3−i3i3i3−i31-1-1100-22-22001-1i3−i3i3−i3i3−i3−i3i31-11-11-11-100000000000000
χ632-2-2-2-2222-1-222-21111-1-1-12-20000-220000-1-111i3i3−i3−i3i3i3−i3−i3−i3i3i3−i3i3−i3−i3i31-1-1100-22-22001-1−i3i3−i3i3−i3i3i3−i31-11-11-11-100000000000000
χ642-2-2-2-2222-1-222-21111-1-1-12-20000-220000-1-111i3i3−i3−i3i3i3−i3−i3i3−i3−i3i3−i3i3i3−i31-1-11002-22-2001-1−i3i3−i3i3i3−i3−i3i3-11-11-11-1100000000000000
χ652-2-2-2-2222-1-222-21111-1-1-1-2200002-2000011-1-1−i3−i3i3i3i3i3−i3−i3−i3i3i3−i3i3−i3−i3i31-1-11002-2-2200-11i3−i3−i3i3i3−i3−i3i3-11-111-11-100000000000000
χ662-2-2-2-2222-1-222-21111-1-1-1-2200002-2000011-1-1−i3−i3i3i3i3i3−i3−i3i3−i3−i3i3−i3i3i3−i31-1-1100-222-200-11i3−i3−i3i3−i3i3i3−i31-11-1-11-1100000000000000
χ672-2-2-2-2222-1-222-21111-1-1-1-2200002-2000011-1-1i3i3−i3−i3−i3−i3i3i3−i3i3i3−i3i3−i3−i3i31-1-1100-222-200-11−i3i3i3−i3i3−i3−i3i31-11-1-11-1100000000000000
χ682-2-2-2-2222-1-222-21111-1-1-1-2200002-2000011-1-1i3i3−i3−i3−i3−i3i3i3i3−i3−i3i3−i3i3i3−i31-1-11002-2-2200-11−i3i3i3−i3−i3i3i3−i3-11-111-11-100000000000000
χ69444-4-4-4-44400004-44-4-44-400000000000000000000000000000000000000000000000000000000000000000000000022−2200
χ70444-4-4-4-44400004-44-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000−222200
χ7144-44-44-4-444-44-444-4-4-4-4400000000000000000000000000000000-4-4440000000000000000000000000000000000000000
χ7244-44-44-4-4-24-44-4-2-22222-20000000000000000000000002323−23−23−23−23232322-2-20000000000000000000000000000000000000000
χ7344-44-44-4-4-24-44-4-2-22222-2000000000000000000000000−23−2323232323−23−2322-2-20000000000000000000000000000000000000000
χ7444-44-44-4-4-2-44-44-2-22222-2000000004i4i−4i−4i000000000000−2i−2i2i2i−2i−2i2i2i-2-2220000000000000000000000000000000000000000
χ7544-44-44-4-4-2-44-44-2-22222-200000000−4i−4i4i4i0000000000002i2i−2i−2i2i2i−2i−2i-2-2220000000000000000000000000000000000000000
χ7644-4-44-44-4400004-4-444-4-4004-40000000000004-44-400000000000000000000000000000000000000000000000000000000
χ7744-4-44-44-4400004-4-444-4-400-44000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ7844-4-44-44-4-20000-222-2-222004-400000000−2i32i3−2i32i3-22-22−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ7944-4-44-44-4-20000-222-2-222004-4000000002i3−2i32i3−2i3-22-222i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ8044-4-44-44-4-20000-222-2-22200-4400000000−2i32i3−2i32i32-22-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ8144-4-44-44-4-20000-222-2-22200-44000000002i3−2i32i3−2i32-22-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ824-444-4-44-440000-444-44-4-400004-4000000000000004-4-440000000000000000000000000000000000000000000000000000
χ834-444-4-44-440000-444-44-4-40000-4400000000000000-444-40000000000000000000000000000000000000000000000000000
χ844-444-4-44-4-200002-2-22-22200004-4000000−2i32i32i3−2i3−2i32i32i3−2i3-222-20000000000000000000000000000000000000000000000000000
χ854-444-4-44-4-200002-2-22-22200004-40000002i3−2i3−2i32i32i3−2i3−2i32i3-222-20000000000000000000000000000000000000000000000000000
χ864-444-4-44-4-200002-2-22-2220000-44000000−2i32i32i3−2i32i3−2i3−2i32i32-2-220000000000000000000000000000000000000000000000000000
χ874-444-4-44-4-200002-2-22-2220000-440000002i3−2i3−2i32i3−2i32i32i3−2i32-2-220000000000000000000000000000000000000000000000000000
χ884-44-444-4-4444-4-4-4-444-4-4400000000000000000000000000000000-44-440000000000000000000000000000000000000000
χ894-44-444-4-4-244-4-422-2-222-200000000000000000000000023−2323−23−2323−23232-22-20000000000000000000000000000000000000000
χ904-44-444-4-4-244-4-422-2-222-2000000000000000000000000−2323−232323−2323−232-22-20000000000000000000000000000000000000000
χ914-44-444-4-4-2-4-44422-2-222-2000000004i−4i4i−4i000000000000−2i2i−2i2i−2i2i−2i2i-22-220000000000000000000000000000000000000000
χ924-44-444-4-4-2-4-44422-2-222-200000000−4i4i−4i4i0000000000002i−2i2i−2i2i−2i2i−2i-22-220000000000000000000000000000000000000000
χ934-4-444-4-4440000-44-44-44-40000000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ944-4-444-4-4440000-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ95888-8-8-8-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000000000

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