Finite Group Databasebeta

← Group #10855128

Character table — Group #10855128

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666662244444444446666121212121212121212121212121212121212121224444444661212121212121212121212121212121244448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ911111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11
χ1011111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-11
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11-1
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-1-11
χ17222222222-2-2-2-2222222222-2-22222000022222222-2-2-2-2222200000000-2-2000000-2-2-2-200000000-2-2000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000222200000000-2-2000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-20000-2-2-2-2-2-2-2-2-2-2-2-2222200000000-22000000-2-2220000000022000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2220000-2-2-2-22222-2-2-2-2-2-2-2-2000000002-200000022-2-20000000022000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-111111111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111111111-1-1-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-1111111111111-2-22222-2-21111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-222-2-2-1-111-1-1-1-1111111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-222-2-222-1-1111111-1-1-1-111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2222-2-2-2-211-1-11111-1-1-1-111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-21111-1-1-1-1-1-1-1-1111111111111-22-2-2222211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222220000-1-1-1-1-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-2-20000001111−i3−i3i3i3−i3−i3i3i311−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222220000-1-1-1-1-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-2-20000001111i3i3−i3−i3i3i3−i3−i311i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i322000000-1-1-1-1i3i3−i3−i3i3i3−i3−i311−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i322000000-1-1-1-1−i3−i3i3i3−i3−i3i3i311i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-20000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-2200000011-1-1−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-20000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-2200000011-1-1i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i32-2000000-1-111i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i32-2000000-1-111−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ3722-222-2-2-22-22-222-2-22-22-2000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000002i−2i0000002-20000
χ3822-222-2-2-22-22-222-2-22-22-2000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000−2i2i000000-220000
χ3922-222-2-2-22-22-222-2-22-22-200000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000002i−2i000000-220000
χ4022-222-2-2-22-22-222-2-22-22-200000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−2i2i0000002-20000
χ412-22-222-2-222-2-22-222-2-22-22-22-200002i−2i2i−2i22-2-200002-22-200002i−2i2i−2i2i−2i2i−2i0000002i−2i0000000000002-22i−2i2i−2i00000000000000
χ422-22-222-2-222-2-22-222-2-22-22-22-20000−2i2i−2i2i22-2-200002-22-20000−2i2i−2i2i−2i2i−2i2i000000−2i2i0000000000002-2−2i2i−2i2i00000000000000
χ432-22-222-2-222-2-22-222-2-22-2-22-2200002i−2i2i−2i-2-22200002-22-200002i−2i2i−2i2i−2i2i−2i000000−2i2i000000000000-22−2i2i−2i2i00000000000000
χ442-22-222-2-222-2-22-222-2-22-2-22-220000−2i2i−2i2i-2-22200002-22-20000−2i2i−2i2i−2i2i−2i2i0000002i−2i000000000000-222i−2i2i−2i00000000000000
χ452-22-222-2-22-222-2-222-2-22-22-2-220000000022-2-20000-22-22000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i-22000000000000000000
χ462-22-222-2-22-222-2-222-2-22-22-2-220000000022-2-20000-22-2200000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i-22000000000000000000
χ472-22-222-2-22-222-2-222-2-22-2-222-200000000-2-2220000-22-22000000000000002i−2i−2i2i000000−2i2i−2i2i2i−2i2i−2i2-2000000000000000000
χ482-22-222-2-22-222-2-222-2-22-2-222-200000000-2-2220000-22-2200000000000000−2i2i2i−2i0000002i−2i2i−2i−2i2i−2i2i2-2000000000000000000
χ492-22-222-2-2-12-2-221-1-111-112-22-200002i−2i2i−2i-1-111−i3−i3i3i3-11-11−i3−i3i3i3−ii−ii−ii−ii0000002i−2i−i3i3−i3i33−3−333−3−33-11−ii−ii00000000000000
χ502-22-222-2-2-12-2-221-1-111-112-22-200002i−2i2i−2i-1-111i3i3−i3−i3-11-11i3i3−i3−i3−ii−ii−ii−ii0000002i−2ii3−i3i3−i3−333−3−333−3-11−ii−ii00000000000000
χ512-22-222-2-2-12-2-221-1-111-112-22-20000−2i2i−2i2i-1-111−i3−i3i3i3-11-11−i3−i3i3i3i−ii−ii−ii−i000000−2i2i−i3i3−i3i3−333−3−333−3-11i−ii−i00000000000000
χ522-22-222-2-2-12-2-221-1-111-112-22-20000−2i2i−2i2i-1-111i3i3−i3−i3-11-11i3i3−i3−i3i−ii−ii−ii−i000000−2i2ii3−i3i3−i33−3−333−3−33-11i−ii−i00000000000000
χ532-22-222-2-2-12-2-221-1-111-11-22-2200002i−2i2i−2i11-1-1−i3−i3i3i3-11-11i3i3−i3−i3−ii−ii−ii−ii000000−2i2ii3−i3−i3i3−333−33−3−331-1i−ii−i00000000000000
χ542-22-222-2-2-12-2-221-1-111-11-22-2200002i−2i2i−2i11-1-1i3i3−i3−i3-11-11−i3−i3i3i3−ii−ii−ii−ii000000−2i2i−i3i3i3−i33−3−33−333−31-1i−ii−i00000000000000
χ552-22-222-2-2-12-2-221-1-111-11-22-220000−2i2i−2i2i11-1-1−i3−i3i3i3-11-11i3i3−i3−i3i−ii−ii−ii−i0000002i−2ii3−i3−i3i33−3−33−333−31-1−ii−ii00000000000000
χ562-22-222-2-2-12-2-221-1-111-11-22-220000−2i2i−2i2i11-1-1i3i3−i3−i3-11-11−i3−i3i3i3i−ii−ii−ii−i0000002i−2i−i3i3i3−i3−333−33−3−331-1−ii−ii00000000000000
χ572-22-222-2-2-1-222-21-1-111-112-2-2200000000-1-111−i3−i3i3i31-11-1−i3−i3i3i33−33−3−33−33002i−2i2i−2i00i3−i3i3−i3−ii−ii−ii−ii1-13−3−3300000000000000
χ582-22-222-2-2-1-222-21-1-111-112-2-2200000000-1-111−i3−i3i3i31-11-1−i3−i3i3i3−33−333−33−300−2i2i−2i2i00i3−i3i3−i3i−ii−ii−ii−i1-1−333−300000000000000
χ592-22-222-2-2-1-222-21-1-111-112-2-2200000000-1-111i3i3−i3−i31-11-1i3i3−i3−i33−33−3−33−3300−2i2i−2i2i00−i3i3−i3i3i−ii−ii−ii−i1-13−3−3300000000000000
χ602-22-222-2-2-1-222-21-1-111-112-2-2200000000-1-111i3i3−i3−i31-11-1i3i3−i3−i3−33−333−33−3002i−2i2i−2i00−i3i3−i3i3−ii−ii−ii−ii1-1−333−300000000000000
χ612-22-222-2-2-1-222-21-1-111-11-222-20000000011-1-1−i3−i3i3i31-11-1i3i3−i3−i33−33−3−33−33002i−2i−2i2i00−i3i3i3−i3i−ii−i−ii−ii-11−333−300000000000000
χ622-22-222-2-2-1-222-21-1-111-11-222-20000000011-1-1−i3−i3i3i31-11-1i3i3−i3−i3−33−333−33−300−2i2i2i−2i00−i3i3i3−i3−ii−iii−ii−i-113−3−3300000000000000
χ632-22-222-2-2-1-222-21-1-111-11-222-20000000011-1-1i3i3−i3−i31-11-1−i3−i3i3i33−33−3−33−3300−2i2i2i−2i00i3−i3−i3i3−ii−iii−ii−i-11−333−300000000000000
χ642-22-222-2-2-1-222-21-1-111-11-222-20000000011-1-1i3i3−i3−i31-11-1−i3−i3i3i3−33−333−33−3002i−2i−2i2i00i3−i3−i3i3i−ii−i−ii−ii-113−3−3300000000000000
χ652-2-2-22-2222-2-222-2-2-2-2222000000002-2-22000000002-2-2200002-2-222-2-2200000000000000000000000000002-20000002-200
χ662-2-2-22-2222-2-222-2-2-2-2222000000002-2-22000000002-2-2200002-2-222-2-220000000000000000000000000000-22000000-2200
χ672-2-2-22-2222-2-222-2-2-2-222200000000-222-2000000002-2-220000-222-2-222-200000000000000000000000000002-2000000-2200
χ682-2-2-22-2222-2-222-2-2-2-222200000000-222-2000000002-2-220000-222-2-222-20000000000000000000000000000-220000002-200
χ69444-4-4-4-444000044-4-4-4-440000004i−4i000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-444000044-4-4-4-44000000−4i4i00000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-20000-2-22222-20000004i−4i0000−2i32i3−2i32i3−2i2i−2i2i000023−2323−23000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-20000-2-22222-20000004i−4i00002i3−2i32i3−2i3−2i2i−2i2i0000−2323−2323000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-20000-2-22222-2000000−4i4i0000−2i32i3−2i32i32i−2i2i−2i0000−2323−2323000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-20000-2-22222-2000000−4i4i00002i3−2i32i3−2i32i−2i2i−2i000023−2323−23000000000000000000000000000000000000000000000000
χ7544-444-4-4-444-44-44-4-44-44-400000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ7644-444-4-4-4-24-44-4-222-22-220000000000000000000022-2-200002323−23−23−23−2323230000000000000000000000000000000000000000
χ7744-444-4-4-4-24-44-4-222-22-220000000000000000000022-2-20000−23−2323232323−23−230000000000000000000000000000000000000000
χ7844-444-4-4-4-2-44-44-222-22-22000000004i4i−4i−4i00000000-2-2220000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ7944-444-4-4-4-2-44-44-222-22-2200000000−4i−4i4i4i00000000-2-22200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ8044-4-4-444-4400004-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000−2i22i2000000
χ8144-4-4-444-4400004-44-44-4-4000000000000000000000000000000000000000000000000000000000000000000002i2−2i2000000
χ824-444-4-44-440000-44-444-4-400004i−4i0000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ834-444-4-44-440000-44-444-4-40000−4i4i000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ844-444-4-44-4-200002-22-2-22200004i−4i000000−2i32i32i3−2i323−23−23230000−2i2i2i−2i000000000000000000000000000000000000000000000000
χ854-444-4-44-4-200002-22-2-22200004i−4i0000002i3−2i3−2i32i3−232323−230000−2i2i2i−2i000000000000000000000000000000000000000000000000
χ864-444-4-44-4-200002-22-2-2220000−4i4i000000−2i32i32i3−2i3−232323−2300002i−2i−2i2i000000000000000000000000000000000000000000000000
χ874-444-4-44-4-200002-22-2-2220000−4i4i0000002i3−2i3−2i32i323−23−232300002i−2i−2i2i000000000000000000000000000000000000000000000000
χ884-4-44-44-4440000-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000022−2200000000
χ894-4-44-44-4440000-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000−222200000000
χ904-4-4-44-444444-4-4-4-4-4-444400000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ914-4-4-44-444-244-4-42222-2-2-2000000000000000000002-2-220000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ924-4-4-44-444-244-4-42222-2-2-2000000000000000000002-2-2200002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ934-4-4-44-444-2-4-4442222-2-2-2000000004-4-4400000000-222-20000-222-2-222-20000000000000000000000000000000000000000
χ944-4-4-44-444-2-4-4442222-2-2-200000000-444-400000000-222-200002-2-222-2-220000000000000000000000000000000000000000
χ9588-8-8-888-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-88-88-4000044-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000

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