Finite Group Databasebeta

← Group #10875908

Character table — Group #10875908

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666622224444444466666666121212121212121212121212121212124444444412121212121212121212121212121212121244448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11-1
χ6111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ7111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11
χ8111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ1111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-111111111-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111-1
χ17222222222-2-2-2-2222222200002222-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-2-2-22000000-2-2-2222200000000000000000000000000
χ18222222222-2-2-2-22222222000022-2-2-2-22200000000-2-2-2-2-2-2-2-2-2-2-2-22222-200000022222-2-200000000000000000000000000
χ19222222222-2-2-2-222222220000-2-222222200000000-2-2-2-2222222222222-2000000-2-2-2-2-2-2-200000000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-222-2-200000000-2-2-2-2-2-2-2-22222-2-2-2-22000000222-2-22200000000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-2-2-222-2-2-211-1-1111111-1-1-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-222-2-2-2-22-1-11111-1-1-1-11111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12-2-2-2-222-21111-1-111111111-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-22-1-1-1-1-1-111111111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-222-2-211111111-1-1-1-11111-1-1-1-11111-222-2-222-211-1-111-1-1-1-11111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-222222-1-111111111-1-1-1-1-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22211111111-1-1-1-111111111-1-1-1-122222-2-2-21111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2-2-2−i3−i3−i3−i3i3i3i3i31111-1-1-1-1111111112000000-211-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-100002222-2-2-2-2i3i3i3i3−i3−i3−i3−i31111-1-1-1-1111111112000000-211-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-2-2-222−i3−i3−i3−i3i3i3i3i3111111111111-1-1-1-1-20000002-1-1-1-111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-1000022-2-2-2-222i3i3i3i3−i3−i3−i3−i3111111111111-1-1-1-1-20000002-1-1-1-111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2222222−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-1-1-1-1-1-1-1-1-2000000-2111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2222222i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-1-1-1-1-1-1-1-1-2000000-2111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-222-2-2−i3−i3−i3−i3i3i3i3i311111111-1-1-1-1111120000002-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-10000-2-2-2-222-2-2i3i3i3i3−i3−i3−i3−i311111111-1-1-1-1111120000002-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ37222-22-2-2-2222-2-2-2-22-22-2222-2-20000000022-2-222-2-222-2-2000000000000000000000000000000000000002i−2i0000002i−2i0000
χ38222-22-2-2-2222-2-2-2-22-22-2222-2-20000000022-2-222-2-222-2-200000000000000000000000000000000000000−2i2i000000−2i2i0000
χ39222-22-2-2-2222-2-2-2-22-22-22-2-22200000000-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i000000−2i2i0000
χ40222-22-2-2-2222-2-2-2-22-22-22-2-22200000000-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i0000002i−2i0000
χ4122-22-2-2-2222-2-22-2-222-22-200002i−2i002i−2i00000000002-22-200002i2i−2i−2i000002-2002i−2i0002i−2i002-22-200002i−2i2i−2i00000000000000
χ4222-22-2-2-2222-2-22-2-222-22-200002i−2i002i−2i00000000002-22-200002i2i−2i−2i00000-2200−2i2i0002i−2i00-22-220000−2i2i−2i2i00000000000000
χ4322-22-2-2-2222-2-22-2-222-22-20000−2i2i00−2i2i00000000002-22-20000−2i−2i2i2i000002-200−2i2i000−2i2i002-22-20000−2i2i−2i2i00000000000000
χ4422-22-2-2-2222-2-22-2-222-22-20000−2i2i00−2i2i00000000002-22-20000−2i−2i2i2i00000-22002i−2i000−2i2i00-22-2200002i−2i2i−2i00000000000000
χ4522-22-2-2-222-222-2-2-222-22-22-22-22i−2i00−2i2i002-22-22-22-2-22-220000−2i−2i2i2i00000002i−2i000002i−2i0000002i−2i2i−2i000000000000000000
χ4622-22-2-2-222-222-2-2-222-22-22-22-2−2i2i002i−2i002-22-22-22-2-22-2200002i2i−2i−2i0000000−2i2i00000−2i2i000000−2i2i−2i2i000000000000000000
χ4722-22-2-2-222-222-2-2-222-22-2-22-222i−2i00−2i2i00-22-22-22-22-22-220000−2i−2i2i2i0000000−2i2i000002i−2i000000−2i2i−2i2i000000000000000000
χ4822-22-2-2-222-222-2-2-222-22-2-22-22−2i2i002i−2i00-22-22-22-22-22-2200002i2i−2i−2i00000002i−2i00000−2i2i0000002i−2i2i−2i000000000000000000
χ4922-22-2-2-22-12-2-2211-1-11-1100002i−2i002i−2i00−i3i3−i3i3i3−i3i3−i3-11-11−i3−i3i3i3−i−iii33−3−302-2002i−2i0−i3i3−ii3−3-11-113−3−33−ii−ii00000000000000
χ5022-22-2-2-22-12-2-2211-1-11-1100002i−2i002i−2i00−i3i3−i3i3i3−i3i3−i3-11-11i3i3−i3−i3−i−iii−3−3330-2200−2i2i0i3−i3−ii−331-11-13−3−33i−ii−i00000000000000
χ5122-22-2-2-22-12-2-2211-1-11-1100002i−2i002i−2i00i3−i3i3−i3−i3i3−i3i3-11-11−i3−i3i3i3−i−iii33−3−30-2200−2i2i0−i3i3−ii3−31-11-1−333−3i−ii−i00000000000000
χ5222-22-2-2-22-12-2-2211-1-11-1100002i−2i002i−2i00i3−i3i3−i3−i3i3−i3i3-11-11i3i3−i3−i3−i−iii−3−33302-2002i−2i0i3−i3−ii−33-11-11−333−3−ii−ii00000000000000
χ5322-22-2-2-22-12-2-2211-1-11-110000−2i2i00−2i2i00−i3i3−i3i3i3−i3i3−i3-11-11−i3−i3i3i3ii−i−i−3−33302-200−2i2i0−i3i3i−i−33-11-11−333−3i−ii−i00000000000000
χ5422-22-2-2-22-12-2-2211-1-11-110000−2i2i00−2i2i00−i3i3−i3i3i3−i3i3−i3-11-11i3i3−i3−i3ii−i−i33−3−30-22002i−2i0i3−i3i−i3−31-11-1−333−3−ii−ii00000000000000
χ5522-22-2-2-22-12-2-2211-1-11-110000−2i2i00−2i2i00i3−i3i3−i3−i3i3−i3i3-11-11−i3−i3i3i3ii−i−i−3−3330-22002i−2i0−i3i3i−i−331-11-13−3−33−ii−ii00000000000000
χ5622-22-2-2-22-12-2-2211-1-11-110000−2i2i00−2i2i00i3−i3i3−i3−i3i3−i3i3-11-11i3i3−i3−i3ii−i−i33−3−302-200−2i2i0i3−i3i−i3−3-11-113−3−33i−ii−i00000000000000
χ5722-22-2-2-22-1-222-211-1-11-112-22-22i−2i00−2i2i00-11-11-11-111-11-1−i3−i3i3i3ii−i−i−3−3330002i−2i000i3−i3−ii3−3−i3i3i3−i3−ii−ii3−3−3300000000000000
χ5822-22-2-2-22-1-222-211-1-11-112-22-22i−2i00−2i2i00-11-11-11-111-11-1i3i3−i3−i3ii−i−i33−3−30002i−2i000−i3i3−ii−33i3−i3−i3i3−ii−ii−333−300000000000000
χ5922-22-2-2-22-1-222-211-1-11-112-22-2−2i2i002i−2i00-11-11-11-111-11-1−i3−i3i3i3−i−iii33−3−3000−2i2i000i3−i3i−i−33−i3i3i3−i3i−ii−i−333−300000000000000
χ6022-22-2-2-22-1-222-211-1-11-112-22-2−2i2i002i−2i00-11-11-11-111-11-1i3i3−i3−i3−i−iii−3−333000−2i2i000−i3i3i−i3−3i3−i3−i3i3i−ii−i3−3−3300000000000000
χ6122-22-2-2-22-1-222-211-1-11-11-22-222i−2i00−2i2i001-11-11-11-11-11-1−i3−i3i3i3ii−i−i−3−333000−2i2i000i3−i3−ii3−3i3−i3−i3i3i−ii−i−333−300000000000000
χ6222-22-2-2-22-1-222-211-1-11-11-22-222i−2i00−2i2i001-11-11-11-11-11-1i3i3−i3−i3ii−i−i33−3−3000−2i2i000−i3i3−ii−33−i3i3i3−i3i−ii−i3−3−3300000000000000
χ6322-22-2-2-22-1-222-211-1-11-11-22-22−2i2i002i−2i001-11-11-11-11-11-1−i3−i3i3i3−i−iii33−3−30002i−2i000i3−i3i−i−33i3−i3−i3i3−ii−ii3−3−3300000000000000
χ6422-22-2-2-22-1-222-211-1-11-11-22-22−2i2i002i−2i001-11-11-11-11-11-1i3i3−i3−i3−i−iii−3−3330002i−2i000−i3i3i−i3−3−i3i3i3−i3−ii−ii−333−300000000000000
χ6522-2-2-222-22-22-22222-2-2-2-22-2-22000000002-2-222-2-22-222-200000000000000000000000000000000000000002i−2i2i−2i00000000
χ6622-2-2-222-22-22-22222-2-2-2-22-2-22000000002-2-222-2-22-222-20000000000000000000000000000000000000000−2i2i−2i2i00000000
χ6722-2-2-222-22-22-22222-2-2-2-2-222-200000000-222-2-222-2-222-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ6822-2-2-222-22-22-22222-2-2-2-2-222-200000000-222-2-222-2-222-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ69444-44-4-4-44-4-444-4-44-44-4400000000000000000000-4-4440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-244-4-422-22-22-244-4-400000000-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ71444-44-4-4-4-244-4-422-22-22-2-4-4440000000022-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-2-4-44422-22-22-2000000000000−2i3−2i32i32i32i32i3−2i3−2i322-2-20000000000000000000000000000000000000000000000000000
χ73444-44-4-4-4-2-4-44422-22-22-20000000000002i32i3−2i3−2i3−2i3−2i32i32i322-2-20000000000000000000000000000000000000000000000000000
χ7444-4-4-444-444-44-4444-4-4-4-4000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-24-44-4-2-2-22222000000000000−2i32i32i3−2i32i3−2i3−2i32i3-222-20000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-24-44-4-2-2-222220000000000002i3−2i3−2i32i3−2i32i32i3−2i3-222-20000000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-2-44-44-2-2-222224-4-4400000000-222-2-222-22-2-220000000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-2-44-44-2-2-22222-444-4000000002-2-222-2-222-2-220000000000000000000000000000000000000000000000000000
χ794-444-44-4-4400004-4-4-444-400000000004i−4i000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ804-444-44-4-4400004-4-4-444-40000000000−4i4i00000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ814-444-44-4-4-20000-2222-2-2200000000004i−4i000000000000−2i32i3−2i32i323−2323−23−2i2i−2i2i0000000000000000000000000000000000000000
χ824-444-44-4-4-20000-2222-2-2200000000004i−4i0000000000002i3−2i32i3−2i3−2323−2323−2i2i−2i2i0000000000000000000000000000000000000000
χ834-444-44-4-4-20000-2222-2-220000000000−4i4i000000000000−2i32i3−2i32i3−2323−23232i−2i2i−2i0000000000000000000000000000000000000000
χ844-444-44-4-4-20000-2222-2-220000000000−4i4i0000000000002i3−2i32i3−2i323−2323−232i−2i2i−2i0000000000000000000000000000000000000000
χ854-44-4-4-44440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ864-44-4-4-44440000-44-444-4-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ874-4-444-44-440000-44-4-4-4440000004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-444-44-440000-44-4-4-444000000-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ894-4-444-44-4-200002-2222-2-20000004-40000000000000000-222-2−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ904-4-444-44-4-200002-2222-2-20000004-40000000000000000-222-22i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ914-4-444-44-4-200002-2222-2-2000000-4400000000000000002-2-22−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ924-4-444-44-4-200002-2222-2-2000000-4400000000000000002-2-222i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ934-4-4-444-44400004-4-44-4-440000000000000000000000000000000000000000000000000000000000000000000022−22000000
χ944-4-4-444-44400004-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000−2222000000
χ958-88-8-8-888-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-40000-444-444-40000000000000000000000000000000000000000000000000000000000000000000000000000

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