Finite Group Databasebeta

← Group #10828059

Character table — Group #10828059

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222224444444444444444444444444888888888888888888888888888888882424242424242424242424244848
order12222222344446662224444666666661212121212121212121222224444446666666661212121212121212121212121244444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-111-111-1-1-1-11-1-11111-1-1-1-11111-1-11-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-111-111-1-1-1-11-1-11111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-11-1111-1-1-1-1-1-11111-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-1-11-1111-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-111111111-1-1
χ91111-1-11111111111-111-1-11111-1-111111111-1-11111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11-1
χ101111-1-11111111111-111-1-11111-1-111111111-1-11111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-11
χ111111-1-11111111111-111-1-11111-1-111111111-1-11111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-11
χ121111-1-11111111111-111-1-11111-1-111111111-1-11111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-1111-1
χ131111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-111-11-1111111-1-111-1-1-1-111-111-1-111-1-111-1-1-1-111-11
χ141111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-111-11-1111111-1-111-1-1-1-111-111-1-1-1-111-1-11111-1-11-1
χ151111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-111-1-111-1-1-1-111-1-11111-1-1-1111111-1-1-1-111-1-1111-1
χ161111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-111-1-111-1-1-1-111-1-11111-1-1-11111-1-11111-1-111-1-1-11
χ17222222222-2-2-2-2222200-2-20022220000-2-2-2-2-2-2000002-202-2000020022-2-2000022-2-200-2000000000000000000
χ18222222222-2-2-2-2222200-2-20022220000-2-2-2-2-2-200000-220-220000200-2-2220000-2-22200-2000000000000000000
χ1922222222-12222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-22-2-2-1-1-111111111111111-1-1-11100000000000000
χ2122222222-12222-1-1-12-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-222-222-2-2-2-2-111-1-1-1-11111-1-1-1-111-1111100000000000000
χ2222222222-12222-1-1-12-2-222-2-2-1-1-1-11111-1-1-1-1-1-11111-2-2-22-2-22-222-1111111-1-1-1-11111-1-1-111-1-100000000000000
χ2322222222-1-2-2-2-2-1-1-1200-2-200-1-1-1-1−i3−i3i3i3111111−i3−i3i3i302-202-20000-1−i3i3-1-111−i3i3−i3i3-1-111−i3i31−i3i3−i3i300000000000000
χ2422222222-1-2-2-2-2-1-1-1200-2-200-1-1-1-1−i3−i3i3i3111111−i3−i3i3i30-220-220000-1−i3i311-1-1i3−i3i3−i311-1-1i3−i31−i3i3i3−i300000000000000
χ2522222222-1-2-2-2-2-1-1-1200-2-200-1-1-1-1i3i3−i3−i3111111i3i3−i3−i302-202-20000-1i3−i3-1-111i3−i3i3−i3-1-111i3−i31i3−i3i3−i300000000000000
χ2622222222-1-2-2-2-2-1-1-1200-2-200-1-1-1-1i3i3−i3−i3111111i3i3−i3−i30-220-220000-1i3−i311-1-1−i3i3−i3i311-1-1−i3i31i3−i3−i3i300000000000000
χ27222222-2-222-2-22222-2222-2-2-2-2-222222222-2-2-2-2-2-2-2-22000000-200-222000000000000002-2-20000000000000000
χ28222222-2-222-2-22222-2-2-22-222-2-222-2-2-2-222-2-2-2-22222-2000000200-2-2-2000000000000002220000000000000000
χ29222222-2-22-222-2222-200-2200-2-2220000-2-22222000000020020-2-2-200000022-2-2000022-200-2-200000000000000
χ30222222-2-22-222-2222-200-2200-2-2220000-2-222220000000-200-2022-2000000-2-2220000-2-2-2002200000000000000
χ31222222-2-2-12-2-22-1-1-1-2222-2-2-211-1-1-1-1-1-1-1-1111111112000000-2001-1-1−i3i3−i3i3−i3i3i3−i3−i3i3−i3i3−i3i3-111i3−i300000000000000
χ32222222-2-2-12-2-22-1-1-1-2222-2-2-211-1-1-1-1-1-1-1-1111111112000000-2001-1-1i3−i3i3−i3i3−i3−i3i3i3−i3i3−i3i3−i3-111−i3i300000000000000
χ33222222-2-2-12-2-22-1-1-1-2-2-22-22211-1-11111-1-11111-1-1-1-1-2000000200111−i3i3−i3i3i3−i3−i3i3−i3i3−i3i3i3−i3-1-1-1−i3i300000000000000
χ34222222-2-2-12-2-22-1-1-1-2-2-22-22211-1-11111-1-11111-1-1-1-1-2000000200111i3−i3i3−i3−i3i3i3−i3i3−i3i3−i3−i3i3-1-1-1i3−i300000000000000
χ35222222-2-2-1-222-2-1-1-1-200-220011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i300020020-2-21−i3i3−i3i3i3−i3-1-111−i3i3i3−i3-1-11i3−i31100000000000000
χ36222222-2-2-1-222-2-1-1-1-200-220011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i3000-200-20221−i3i3i3−i3−i3i311-1-1i3−i3−i3i3111i3−i3-1-100000000000000
χ37222222-2-2-1-222-2-1-1-1-200-220011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i300020020-2-21i3−i3i3−i3−i3i3-1-111i3−i3−i3i3-1-11−i3i31100000000000000
χ38222222-2-2-1-222-2-1-1-1-200-220011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i3000-200-20221i3−i3−i3i3i3−i311-1-1−i3i3i3−i3111−i3i3-1-100000000000000
χ392222-2-2222-2-2-2-2222-200220022-2-20000-2-2-2-222000002-20-220000-20022-2-20000-2-222002000000000000000000
χ402222-2-2222-2-2-2-2222-200220022-2-20000-2-2-2-22200000-2202-20000-200-2-222000022-2-2002000000000000000000
χ412222-2-222-12222-1-1-1-222-2-222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-2222-2-2-2-22-2111-1-1-1-1-1-111111111111-1-100000000000000
χ422222-2-222-12222-1-1-1-222-2-222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-2-2-2-2222-2-22111111111-1-1-1-1-1-1-1-11111100000000000000
χ432222-2-222-12222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-1111111222-2-2-222-221-1-1-1-1-1-111-1-11111-1-11-1-11100000000000000
χ442222-2-222-12222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-11111112-2-2222-222-21-1-11111-1-111-1-1-1-1111-1-1-1-100000000000000
χ452222-2-222-1-2-2-2-2-1-1-1-2002200-1-111−i3−i3i3i31111-1-1−i3−i3i3i302-20-2200001i3−i3-1-111−i3i3i3−i311-1-1i3−i3-1i3−i3−i3i300000000000000
χ462222-2-222-1-2-2-2-2-1-1-1-2002200-1-111−i3−i3i3i31111-1-1−i3−i3i3i30-2202-200001i3−i311-1-1i3−i3−i3i3-1-111−i3i3-1i3−i3i3−i300000000000000
χ472222-2-222-1-2-2-2-2-1-1-1-2002200-1-111i3i3−i3−i31111-1-1i3i3−i3−i302-20-2200001−i3i3-1-111i3−i3−i3i311-1-1−i3i3-1−i3i3i3−i300000000000000
χ482222-2-222-1-2-2-2-2-1-1-1-2002200-1-111i3i3−i3−i31111-1-1i3i3−i3−i30-2202-200001−i3i311-1-1−i3i3i3−i3-1-111i3−i3-1−i3i3−i3i300000000000000
χ492222-2-2-2-222-2-22222222-22-2-2-2-2-2-2222222-2-222-2-2-2-2-20000002002-2-200000000000000-2220000000000000000
χ502222-2-2-2-222-2-222222-2-2-2222-2-2-2-2-2-2-2-222-2-22222222000000-20022200000000000000-2-2-20000000000000000
χ512222-2-2-2-22-222-22222002-200-2-2-2-20000-2-222-2-20000000200-20-22200000022220000-2-2200-2-200000000000000
χ522222-2-2-2-22-222-22222002-200-2-2-2-20000-2-222-2-20000000-200202-22000000-2-2-2-20000222002200000000000000
χ532222-2-2-2-2-12-2-22-1-1-1222-22-2-21111-1-1-1-1-1-111-1-11111-2000000200-111−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i31-1-1i3−i300000000000000
χ542222-2-2-2-2-12-2-22-1-1-1222-22-2-21111-1-1-1-1-1-111-1-11111-2000000200-111i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i31-1-1−i3i300000000000000
χ552222-2-2-2-2-12-2-22-1-1-12-2-2-222211111111-1-111-1-1-1-1-1-12000000-200-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3111−i3i300000000000000
χ562222-2-2-2-2-12-2-22-1-1-12-2-2-222211111111-1-111-1-1-1-1-1-12000000-200-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3111i3−i300000000000000
χ572222-2-2-2-2-1-222-2-1-1-12002-2001111−i3−i3i3i311-1-111i3i3−i3−i3000200-20-22-1i3−i3−i3i3i3−i3-1-1-1-1i3−i3−i3i311-1−i3i31100000000000000
χ582222-2-2-2-2-1-222-2-1-1-12002-2001111−i3−i3i3i311-1-111i3i3−i3−i3000-200202-2-1i3−i3i3−i3−i3i31111−i3i3i3−i3-1-1-1−i3i3-1-100000000000000
χ592222-2-2-2-2-1-222-2-1-1-12002-2001111i3i3−i3−i311-1-111−i3−i3i3i3000200-20-22-1−i3i3i3−i3−i3i3-1-1-1-1−i3i3i3−i311-1i3−i31100000000000000
χ602222-2-2-2-2-1-222-2-1-1-12002-2001111i3i3−i3−i311-1-111−i3−i3i3i3000-200202-2-1−i3i3−i3i3i3−i31111i3−i3−i3i3-1-1-1i3−i3-1-100000000000000
χ612-22-2002-2222-2-2-2-2202-2002-22-2002-22-22-22-2002-22-200000000000000000000000000000000002i−2i0000002i−2i00
χ622-22-2002-2222-2-2-2-2202-2002-22-2002-22-22-22-2002-22-20000000000000000000000000000000000−2i2i000000−2i2i00
χ632-22-2002-2222-2-2-2-220-2200-222-200-22-222-22-200-22-2200000000000000000000000000000000002i−2i000000−2i2i00
χ642-22-2002-2222-2-2-2-220-2200-222-200-22-222-22-200-22-220000000000000000000000000000000000−2i2i0000002i−2i00
χ652-22-200-2222-22-2-2-2202-200-22-22002-22-22-2-2200-22-22000000000000000000000000000000002i−2i0000002i−2i0000
χ662-22-200-2222-22-2-2-2202-200-22-22002-22-22-2-2200-22-2200000000000000000000000000000000−2i2i000000−2i2i0000
χ672-22-200-2222-22-2-2-220-22002-2-2200-22-222-2-22002-22-2000000000000000000000000000000002i−2i000000−2i2i0000
χ682-22-200-2222-22-2-2-220-22002-2-2200-22-222-2-22002-22-200000000000000000000000000000000−2i2i0000002i−2i0000
χ6944-4-44-40040000-44-40000000004-4000000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ7044-4-44-40040000-44-40000000004-400000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ7144-4-4-440040000-44-4000000000-44000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ7244-4-4-440040000-44-4000000000-4400000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ734-44-4004-44-4-444-4-4400000004-4000000-44-440000000000000000000000000000000000000000000000000000
χ744-44-4004-4-244-4-422-204-4004-4-2200-22-22-22-2200-22-220000000000000000000000000000000000000000000000
χ754-44-4004-4-244-4-422-20-4400-44-22002-22-2-22-22002-22-20000000000000000000000000000000000000000000000
χ764-44-4004-4-2-4-44422-20000000-2200−2i32i32i3−2i32-22-200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ774-44-4004-4-2-4-44422-20000000-22002i3−2i3−2i32i32-22-2002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-44-400-444-44-44-4-440000000-44000000-444-40000000000000000000000000000000000000000000000000000
χ794-44-400-44-24-44-422-204-400-442-200-22-22-222-2002-22-20000000000000000000000000000000000000000000000
χ804-44-400-44-24-44-422-20-44004-42-2002-22-2-222-200-22-220000000000000000000000000000000000000000000000
χ814-44-400-44-2-44-4422-200000002-200−2i32i32i3−2i32-2-22002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ824-44-400-44-2-44-4422-200000002-2002i3−2i3−2i32i32-2-2200−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ8388-8-88-800-400004-44000000000-44000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8800-400004-440000000004-4000000000000000000000000000000000000000000000000000000000000
χ858-8-880000800008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-880000-40000-444000000000000000000043−4300000000000000000000000000000000000000000000000000
χ878-8-880000-40000-4440000000000000000000−434300000000000000000000000000000000000000000000000000

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