Finite Group Databasebeta

← Group #10843145

Character table — Group #10843145

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222444444444444444444444444444488888888888888888888888888888881212242424242424242424484848
order1222223444466622444444666666881212121212121212242424242224446666668881212121212121212121224242424242488224444888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1111-1-1-1
χ41111111111111111111111111111-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-11-1
χ61111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1111-11
χ71111111111111111-1-1-1-111111111-1-111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11-1-11-11
χ81111111111111111-1-1-1-111111111-1-111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-111-11-1
χ911111111111111-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11
χ1011111111111111-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-111-1
χ1111111111111111-1-11111-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111-1-11111-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-111-1-1-1-1-11111-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-11111-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111-1-11-1-1
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-11111-1-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-111-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11-1-111111-1-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-11-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11-1-111111-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1111-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-11111-2-2-222-2111111-2-2-2-1-1-1-1-1-1-1-11111111100000000000000
χ19222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111112221111111111-1-1-1-1-1-100000000000000
χ20222222-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-11111222-2-22-1-1-1-1-1-1-2-2-211111111-1-111111100000000000000
χ21222222-12222-1-1-1-2-22222-2-2-1-1111122-1-1-11111-1-1-1-1-12-2-2-2-22-1-111112-2-2-1-1-1-11111-1-1-1-1111100000000000000
χ22222222-12222-1-1-1-2-22222-2-2-1-11111-2-2-1-1-11111-11111-222-2-2-211-1-1-1-1-222-1-1-1-111111111-1-1-1-100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1111122-1-1-11111-1-1-1-1-1-22222-211-1-1-1-12-2-21111-1-1-1-111-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-2-2-1-1-11111-111112-2-2222-1-11111-2221111-1-1-1-1-1-111-1-1-1-100000000000000
χ252222-2-222-22-22220022-2-200-2-20000222-2-2000022222-200002-2-20000-20022-2-2000022-2-2000000000000000000
χ262222-2-222-22-22220022-2-200-2-20000-2-22-2-200002-2-2-2-220000-222000020022-2-20000-2-222000000000000000000
χ272222-2-222-22-222200-2-22200-2-20000222-2-200002222220000-2220000-200-2-2220000-2-2-2-2000000000000000000
χ282222-2-222-22-222200-2-22200-2-20000-2-22-2-200002-2-2-2-2-200002-2-20000200-2-22200002222000000000000000000
χ292222-2-22-22-22222220000-2-2-2-2222200-222-2-2-2-2-2000000000000000000000000000000000002200-2200-200000
χ302222-2-22-22-22222220000-2-2-2-2222200-222-2-2-2-2-200000000000000000000000000000000000-2-2002-200200000
χ312222-2-22-22-22222-2-2000022-2-2-2-2-2-200-2222222-20000000000000000000000000000000000022002-200-200000
χ322222-2-22-22-22222-2-2000022-2-2-2-2-2-200-2222222-200000000000000000000000000000000000-2-200-2200200000
χ332222-2-2-12-22-2-1-1-10022-2-20011−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-1-20000211−i3−i3i3i3-200-1-111−i3−i3i3i3-1-111−i3−i3i3i300000000000000
χ342222-2-2-12-22-2-1-1-10022-2-20011−i3−i3i3i3-2-2-111−i3−i3i3i3-1111120000-2-1-1i3i3−i3−i3200-1-111−i3−i3i3i311-1-1i3i3−i3−i300000000000000
χ352222-2-2-12-22-2-1-1-10022-2-20011i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-1-20000211i3i3−i3−i3-200-1-111i3i3−i3−i3-1-111i3i3−i3−i300000000000000
χ362222-2-2-12-22-2-1-1-10022-2-20011i3i3−i3−i3-2-2-111i3i3−i3−i3-1111120000-2-1-1−i3−i3i3i3200-1-111i3i3−i3−i311-1-1−i3−i3i3i300000000000000
χ372222-2-2-12-22-2-1-1-100-2-2220011−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-120000-2-1-1i3i3−i3−i3-20011-1-1i3i3−i3−i31111−i3−i3i3i300000000000000
χ382222-2-2-12-22-2-1-1-100-2-2220011−i3−i3i3i3-2-2-111−i3−i3i3i3-11111-20000211−i3−i3i3i320011-1-1i3i3−i3−i3-1-1-1-1i3i3−i3−i300000000000000
χ392222-2-2-12-22-2-1-1-100-2-2220011i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-120000-2-1-1−i3−i3i3i3-20011-1-1−i3−i3i3i31111i3i3−i3−i300000000000000
χ402222-2-2-12-22-2-1-1-100-2-2220011i3i3−i3−i3-2-2-111i3i3−i3−i3-11111-20000211i3i3−i3−i320011-1-1−i3−i3i3i3-1-1-1-1−i3−i3i3i300000000000000
χ412-2-222-222-2-22-22-22-22i−2i2i−2i2-22-22-22-20022-22-22-2-200000002i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ422-2-222-222-2-22-22-22-2−2i2i−2i2i2-22-22-22-20022-22-22-2-20000000−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ432-2-222-222-2-22-22-2-222i−2i2i−2i-222-2-22-220022-2-22-22-20000000−2i2i00000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ442-2-222-222-2-22-22-2-22−2i2i−2i2i-222-2-22-220022-2-22-22-200000002i−2i0000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ452-2-222-2-12-2-221-112-22i−2i2i−2i2-2-11-11-1100-1-11-11-11133−3−30002i−2i0−i3i3−i3i3−i3i3000−ii−ii−ii−ii−i3i33−33−33−300000000000000
χ462-2-222-2-12-2-221-112-22i−2i2i−2i2-2-11-11-1100-1-11-11-111−3−3330002i−2i0i3−i3i3−i3i3−i3000−ii−ii−ii−iii3−i3−33−33−3300000000000000
χ472-2-222-2-12-2-221-112-2−2i2i−2i2i2-2-11-11-1100-1-11-11-11133−3−3000−2i2i0i3−i3i3−i3i3−i3000i−ii−ii−ii−ii3−i33−33−33−300000000000000
χ482-2-222-2-12-2-221-112-2−2i2i−2i2i2-2-11-11-1100-1-11-11-111−3−333000−2i2i0−i3i3−i3i3−i3i3000i−ii−ii−ii−i−i3i3−33−33−3300000000000000
χ492-2-222-2-12-2-221-11-222i−2i2i−2i-22-111-11-100-1-111-11-1133−3−3000−2i2i0−i3i3i3−i3i3−i3000−ii−iii−ii−i−i3i33−3−33−3300000000000000
χ502-2-222-2-12-2-221-11-222i−2i2i−2i-22-111-11-100-1-111-11-11−3−333000−2i2i0i3−i3−i3i3−i3i3000−ii−iii−ii−ii3−i3−333−33−300000000000000
χ512-2-222-2-12-2-221-11-22−2i2i−2i2i-22-111-11-100-1-111-11-1133−3−30002i−2i0i3−i3−i3i3−i3i3000i−ii−i−ii−iii3−i33−3−33−3300000000000000
χ522-2-222-2-12-2-221-11-22−2i2i−2i2i-22-111-11-100-1-111-11-11−3−3330002i−2i0−i3i3i3−i3i3−i3000i−ii−i−ii−ii−i3i3−333−33−300000000000000
χ532-2-22-22222-2-2-22-2002i−2i−2i2i00-220000002-220000-2000002-2000002-2-2202i−2i2i−2i−2i2i000000002i−2i−2i2i00000000000000
χ542-2-22-22222-2-2-22-2002i−2i−2i2i00-220000002-220000-200000-2200000-222-20−2i2i2i−2i−2i2i00000000−2i2i2i−2i00000000000000
χ552-2-22-22222-2-2-22-200−2i2i2i−2i00-220000002-220000-2000002-2000002-2-220−2i2i−2i2i2i−2i00000000−2i2i2i−2i00000000000000
χ562-2-22-22222-2-2-22-200−2i2i2i−2i00-220000002-220000-200000-2200000-222-202i−2i−2i2i2i−2i000000002i−2i−2i2i00000000000000
χ572-2-22-222-2-222-22-22-20000-22-222-22-200-22-2-22-22200000000000000000000000000000000000002-2000002-2000
χ582-2-22-222-2-222-22-22-20000-22-222-22-200-22-2-22-2220000000000000000000000000000000000000-2200000-22000
χ592-2-22-222-2-222-22-2-2200002-2-22-22-2200-22-22-22-2200000000000000000000000000000000000002-200000-22000
χ602-2-22-222-2-222-22-2-2200002-2-22-22-2200-22-22-22-220000000000000000000000000000000000000-22000002-2000
χ612-2-22-22-122-2-21-11002i−2i−2i2i001-1−i3i3i3−i300-11-1−i3i3i3−i3133−3−302-2000i3−i3-111-102i−2i−iii−i3−3−33−i3i3−33−iii−i00000000000000
χ622-2-22-22-122-2-21-11002i−2i−2i2i001-1−i3i3i3−i300-11-1−i3i3i3−i31−3−3330-22000−i3i31-1-110−2i2i−iii−i3−3−33i3−i33−3i−i−ii00000000000000
χ632-2-22-22-122-2-21-11002i−2i−2i2i001-1i3−i3−i3i300-11-1i3−i3−i3i3133−3−30-22000i3−i31-1-110−2i2i−iii−i−333−3−i3i3−33i−i−ii00000000000000
χ642-2-22-22-122-2-21-11002i−2i−2i2i001-1i3−i3−i3i300-11-1i3−i3−i3i31−3−33302-2000−i3i3-111-102i−2i−iii−i−333−3i3−i33−3−iii−i00000000000000
χ652-2-22-22-122-2-21-1100−2i2i2i−2i001-1−i3i3i3−i300-11-1−i3i3i3−i3133−3−30-22000−i3i31-1-1102i−2ii−i−ii−333−3i3−i3−33−iii−i00000000000000
χ662-2-22-22-122-2-21-1100−2i2i2i−2i001-1−i3i3i3−i300-11-1−i3i3i3−i31−3−33302-2000i3−i3-111-10−2i2ii−i−ii−333−3−i3i33−3i−i−ii00000000000000
χ672-2-22-22-122-2-21-1100−2i2i2i−2i001-1i3−i3−i3i300-11-1i3−i3−i3i3133−3−302-2000−i3i3-111-10−2i2ii−i−ii3−3−33i3−i3−33i−i−ii00000000000000
χ682-2-22-22-122-2-21-1100−2i2i2i−2i001-1i3−i3−i3i300-11-1i3−i3−i3i31−3−3330-22000i3−i31-1-1102i−2ii−i−ii3−3−33−i3i33−3−iii−i00000000000000
χ694444444-4-4-4-44440000000044000000-4-4-40000-40000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-200000000-2-2−2i3−2i32i32i3002222i32i3−2i3−2i320000000000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-200000000-2-22i32i3−2i3−2i300222−2i3−2i32i32i320000000000000000000000000000000000000000000000000
χ724444-4-4-2-44-44-2-2-2440000-4-422-2-2-2-2002-2-2222220000000000000000000000000000000000000000000000000
χ734444-4-4-2-44-44-2-2-2-4-4000044222222002-2-2-2-2-2-220000000000000000000000000000000000000000000000000
χ7444-4-400400004-4-400000000000000−2i22i200000000−2i22i2−2i22i20000000000000000000000000000000−2i22i200002-2000000
χ7544-4-400400004-4-400000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000000000002i2−2i20000-22000000
χ7644-4-400400004-4-4000000000000002i2−2i2000000002i2−2i22i2−2i20000000000000000000000000000000−2i22i20000-22000000
χ7744-4-400400004-4-4000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000002i2−2i200002-2000000
χ784-4-444-44-444-4-44-4000000004-4000000-4-44000040000000000000000000000000000000000000000000000000
χ794-4-444-4-2-444-42-2200000000-22−2i32i32i3−2i30022-22i3−2i3−2i32i3-20000000000000000000000000000000000000000000000000
χ804-4-444-4-2-444-42-2200000000-222i3−2i3−2i32i30022-2−2i32i32i3−2i3-20000000000000000000000000000000000000000000000000
χ814-4-44-44-2-4-4442-224-40000-442-2-22-22002-222-22-2-20000000000000000000000000000000000000000000000000
χ824-4-44-44-2-4-4442-22-4400004-42-22-22-2002-22-22-22-20000000000000000000000000000000000000000000000000
χ8388-8-800-40000-44400000000000000−4i24i2000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ8488-8-800-40000-444000000000000004i2−4i200000000−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ858-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-4000044-40000000000000000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ878-88-800-4000044-4000000000000000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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