Finite Group Databasebeta

← Group #10830088

Character table — Group #10830088

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666644444444444412121212121212121212121212121212121212121212121222224444666666661212121212121212121222448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-11111-1-1111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-2222222222-2-200002222-2-2-2-222220000000022222222000000-2-2000000000000-2-2-2-2-2-200000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2000000220000000000002222-2-200000000000000
χ19222222222-2-2-2-22222222-2-222000022-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000-22000000000000-2-2222200000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-222-2-2-2-2-2-2-2-200000000-2-2-2-222220000002-200000000000022-2-22200000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222-2-211111111-1-1-1-11111-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-22-2-1-1-1-111111111-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-222-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-2-222-2-2-221111-1-1-1-1111111-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-1-1-1-1111111111111-1-1-1-11111-2-222222-21111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-222-1-1-1-11111111111111111-1-1-1-122-2-222-22-1-1-1-11111-1-1-1-111-1-11100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2000022221111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-1-1-1-1-1-1-1-1000000-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311111100000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2000022221111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-1-1-1-1-1-1-1-1000000-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311111100000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-21111-1-1-1-1−i3−i3−i3−i3i3i3i3i31111111100000022i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-1-1-11100000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-21111-1-1-1-1i3i3i3i3−i3−i3−i3−i31111111100000022−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-1-1-11100000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-211111111−i3−i3−i3−i3i3i3i3i3-1-1-1-11111000000-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-1-1-100000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-211111111i3i3i3i3−i3−i3−i3−i3-1-1-1-11111000000-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-1-1-100000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-10000002-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-111-1-100000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-22211111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-10000002-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-111-1-100000000000000
χ372222-2-2-2-22-22-2222-2-22-2-200002i2i−2i−2i000022-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000002-2002i−2i00000000
χ382222-2-2-2-22-22-2222-2-22-2-200002i2i−2i−2i000022-2-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000-2200−2i2i00000000
χ392222-2-2-2-22-22-2222-2-22-2-20000−2i−2i2i2i000022-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000002-200−2i2i00000000
χ402222-2-2-2-22-22-2222-2-22-2-20000−2i−2i2i2i000022-2-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000-22002i−2i00000000
χ412-2-222-2-2222-2-22-2-2-2-22222-22-2000000002-22-222-2-200000000000000002-22-200002-22-22-22-2000000002-200000000000000
χ422-2-222-2-2222-2-22-2-2-2-22222-22-2000000002-22-222-2-20000000000000000-22-220000-22-22-22-22000000002-200000000000000
χ432-2-222-2-2222-2-22-2-2-2-2222-22-22000000002-22-2-2-22200000000000000002-2-2200002-22-2-22-2200000000-2200000000000000
χ442-2-222-2-2222-2-22-2-2-2-2222-22-22000000002-22-2-2-2220000000000000000-222-20000-22-222-22-200000000-2200000000000000
χ452-2-222-2-222-222-2-2-2-2-22222-2-222-22-20000-22-2222-2-22-22-22-22-20000000000002-200000000002-22-20000-2200000000000000
χ462-2-222-2-222-222-2-2-2-2-22222-2-22-22-220000-22-2222-2-2-22-22-22-22000000000000-220000000000-22-220000-2200000000000000
χ472-2-222-2-222-222-2-2-2-2-2222-222-22-22-20000-22-22-2-2222-22-22-22-2000000000000-220000000000-22-2200002-200000000000000
χ482-2-222-2-222-222-2-2-2-2-2222-222-2-22-220000-22-22-2-222-22-22-22-220000000000002-200000000002-22-200002-200000000000000
χ492-2-222-2-22-12-2-221111-1-1-12-22-200000000-11-11-1-111−i3i3−i3i3i3−i3i3−i3−i3−i3i3i3−i3−i3i3i32-22-20000-11-11-11-11−i3i3i3−i3−i3i3−i3i3-1100000000000000
χ502-2-222-2-22-12-2-221111-1-1-12-22-200000000-11-11-1-111−i3i3−i3i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3-22-2200001-11-11-11-1−i3i3i3−i3i3−i3i3−i3-1100000000000000
χ512-2-222-2-22-12-2-221111-1-1-12-22-200000000-11-11-1-111i3−i3i3−i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-22-2200001-11-11-11-1i3−i3−i3i3−i3i3−i3i3-1100000000000000
χ522-2-222-2-22-12-2-221111-1-1-12-22-200000000-11-11-1-111i3−i3i3−i3−i3i3−i3i3i3i3−i3−i3i3i3−i3−i32-22-20000-11-11-11-11i3−i3−i3i3i3−i3i3−i3-1100000000000000
χ532-2-222-2-22-12-2-221111-1-1-1-22-2200000000-11-1111-1-1−i3i3−i3i3i3−i3i3−i3−i3−i3i3i3i3i3−i3−i32-2-220000-11-111-11-1i3−i3−i3i3−i3i3i3−i31-100000000000000
χ542-2-222-2-22-12-2-221111-1-1-1-22-2200000000-11-1111-1-1−i3i3−i3i3i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3-222-200001-11-1-11-11i3−i3−i3i3i3−i3−i3i31-100000000000000
χ552-2-222-2-22-12-2-221111-1-1-1-22-2200000000-11-1111-1-1i3−i3i3−i3−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3-222-200001-11-1-11-11−i3i3i3−i3−i3i3i3−i31-100000000000000
χ562-2-222-2-22-12-2-221111-1-1-1-22-2200000000-11-1111-1-1i3−i3i3−i3−i3i3−i3i3i3i3−i3−i3−i3−i3i3i32-2-220000-11-111-11-1−i3i3i3−i3i3−i3−i3i31-100000000000000
χ572-2-222-2-22-1-222-21111-1-1-12-2-222-22-200001-11-1-1-111-11-11-11-11−i3−i3i3i3−i3−i3i3i300002-200−i3i3i3−i3−i3i3i3−i3-11-11i3−i3i3−i31-100000000000000
χ582-2-222-2-22-1-222-21111-1-1-12-2-222-22-200001-11-1-1-111-11-11-11-11i3i3−i3−i3i3i3−i3−i300002-200i3−i3−i3i3i3−i3−i3i3-11-11−i3i3−i3i31-100000000000000
χ592-2-222-2-22-1-222-21111-1-1-12-2-22-22-2200001-11-1-1-1111-11-11-11-1−i3−i3i3i3−i3−i3i3i30000-2200i3−i3−i3i3i3−i3−i3i31-11-1i3−i3i3−i31-100000000000000
χ602-2-222-2-22-1-222-21111-1-1-12-2-22-22-2200001-11-1-1-1111-11-11-11-1i3i3−i3−i3i3i3−i3−i30000-2200−i3i3i3−i3−i3i3i3−i31-11-1−i3i3−i3i31-100000000000000
χ612-2-222-2-22-1-222-21111-1-1-1-222-22-22-200001-11-111-1-1-11-11-11-11−i3−i3i3i3i3i3−i3−i30000-2200−i3i3i3−i3i3−i3−i3i31-11-1i3−i3−i3i3-1100000000000000
χ622-2-222-2-22-1-222-21111-1-1-1-222-22-22-200001-11-111-1-1-11-11-11-11i3i3−i3−i3−i3−i3i3i30000-2200i3−i3−i3i3−i3i3i3−i31-11-1−i3i3i3−i3-1100000000000000
χ632-2-222-2-22-1-222-21111-1-1-1-222-2-22-2200001-11-111-1-11-11-11-11-1−i3−i3i3i3i3i3−i3−i300002-200i3−i3−i3i3−i3i3i3−i3-11-11i3−i3−i3i3-1100000000000000
χ642-2-222-2-22-1-222-21111-1-1-1-222-2-22-2200001-11-111-1-11-11-11-11-1i3i3−i3−i3−i3−i3i3i300002-200−i3i3i3−i3i3−i3−i3i3-11-11−i3i3i3−i3-1100000000000000
χ652-2-22-222-2222-2-2-2-2222-2-200002i−2i−2i2i0000-222-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002i−2i002-2000000
χ662-2-22-222-2222-2-2-2-2222-2-200002i−2i−2i2i0000-222-200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000−2i2i00-22000000
χ672-2-22-222-2222-2-2-2-2222-2-20000−2i2i2i−2i0000-222-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002i−2i00-22000000
χ682-2-22-222-2222-2-2-2-2222-2-20000−2i2i2i−2i0000-222-20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000−2i2i002-2000000
χ694444-4-4-4-444-44-444-4-44-4-4000000000000-4-444000000000000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-24-44-4-2-222-22200000000000022-2-200002323−23−23−23−232323000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-24-44-4-2-222-22200000000000022-2-20000−23−2323232323−23−23000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-44-44-2-222-22200004i4i−4i−4i0000-2-2220000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ734444-4-4-4-4-2-44-44-2-222-2220000−4i−4i4i4i0000-2-22200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7444-4-444-4-4400004-44-4-44-400000000004i−4i000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7544-4-444-4-4400004-44-4-44-40000000000−4i4i00000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7644-4-444-4-4-20000-22-222-2200000000004i−4i0000−2i32i3−2i32i30000000023−2323−23−2i2i−2i2i0000000000000000000000000000000000000000
χ7744-4-444-4-4-20000-22-222-2200000000004i−4i00002i3−2i32i3−2i300000000−2323−2323−2i2i−2i2i0000000000000000000000000000000000000000
χ7844-4-444-4-4-20000-22-222-220000000000−4i4i0000−2i32i3−2i32i300000000−2323−23232i−2i2i−2i0000000000000000000000000000000000000000
χ7944-4-444-4-4-20000-22-222-220000000000−4i4i00002i3−2i32i3−2i30000000023−2323−232i−2i2i−2i0000000000000000000000000000000000000000
χ8044-4-4-4-444400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000022−2200
χ8144-4-4-4-444400004-4-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000−222200
χ824-44-44-44-440000-44-44-44-4000000004i−4i0000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ834-44-44-44-440000-44-44-44-400000000−4i4i000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ844-44-44-44-4-200002-22-22-22000000004i−4i000000−2i32i32i3−2i300000000−2i2i2i−2i23−23−23230000000000000000000000000000000000000000
χ854-44-44-44-4-200002-22-22-22000000004i−4i0000002i3−2i3−2i32i300000000−2i2i2i−2i−232323−230000000000000000000000000000000000000000
χ864-44-44-44-4-200002-22-22-2200000000−4i4i000000−2i32i32i3−2i3000000002i−2i−2i2i−232323−230000000000000000000000000000000000000000
χ874-44-44-44-4-200002-22-22-2200000000−4i4i0000002i3−2i3−2i32i3000000002i−2i−2i2i23−23−23230000000000000000000000000000000000000000
χ884-44-4-44-4440000-444-4-4-44000000000000000000000000000000000000000000000000000000000000000000000022−220000
χ894-44-4-44-4440000-444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000−22220000
χ904-4-44-444-44-4-444-4-4444-4-40000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-4-244-4-422-2-2-22200004i−4i−4i4i00002-2-220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ924-4-44-444-4-244-4-422-2-2-2220000−4i4i4i−4i00002-2-2200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ934-4-44-444-4-2-4-44422-2-2-222000000000000-222-2000023−23−2323−232323−23000000000000000000000000000000000000000000000000
χ944-4-44-444-4-2-4-44422-2-2-222000000000000-222-20000−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ9588-8-8-8-888-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-88-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000000000

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