Finite Group Databasebeta

← Group #10828640

Character table — Group #10828640

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order12222234444444466666661212121212121212224444444444446666121212121212121212121212121212121212121244444412121212121212121212121212121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-1-1111-11-1
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1111-1-1-11-11
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-111-11-11
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-11-11-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-111-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1722222222222-2-2-2-2222222222222222-2-222-2-200000000-2-2-2-2-2-2-2-200000000000000002-2000022-2-222-2-200000000000000000000
χ1822222222222-2-2-2-2222222222222222-2-2-2-22200000000-2-2-2-2-2-2-2-20000000000000000-220000-2-222-2-22200000000000000000000
χ192222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2000000002222-2-2-2-20000000000000000-22000022-2-2-2-22200000000000000000000
χ202222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222000000002222-2-2-2-200000000000000002-20000-2-22222-2-200000000000000000000
χ21222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ23222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111111111000000000000
χ24222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-20000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-20000-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-20000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-20000-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2220000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2220000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-222222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000
χ30222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000
χ31222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-1000000000000
χ32222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-2-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-1-1-1-11111000000000000
χ33222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ34222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ35222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-22200000000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000000000
χ372222-2-2222-2-222-2-2-2-22-2-2222222-2-2-2-22-200000000000022-2-222-2-200000000000000000000000000000000000000020-2002-20000
χ382222-2-2222-2-222-2-2-2-22-2-2222222-2-2-2-22-200000000000022-2-222-2-2000000000000000000000000000000000000000-20200-220000
χ392222-2-2222-2-2-2-222-2-22-2-2222222-2-2-2-2-22000000000000-2-222-2-2220000000000000000000000000000000000000020-202-2000000
χ402222-2-2222-2-2-2-222-2-22-2-2222222-2-2-2-2-22000000000000-2-222-2-22200000000000000000000000000000000000000-2020-22000000
χ412222-2-22-2-22222-2-2-2-22-2-222-2-2-2-22222-22000000000000-2-22222-2-200000000000000000000000000000000000000020-200-220000
χ422222-2-22-2-22222-2-2-2-22-2-222-2-2-2-22222-22000000000000-2-22222-2-2000000000000000000000000000000000000000-202002-20000
χ432222-2-22-2-222-2-222-2-22-2-222-2-2-2-222222-200000000000022-2-2-2-2220000000000000000000000000000000000000020-20-22000000
χ442222-2-22-2-222-2-222-2-22-2-222-2-2-2-222222-200000000000022-2-2-2-22200000000000000000000000000000000000000-20202-2000000
χ4522-2-2-22200002-22-2-2-2222-2-200000000002i−2i2i−2i000022-2-200002-22-20000000022-2-222-2-200002i−2i2i−2i2i−2i000000002i−2i2i−2i000000000000
χ4622-2-2-22200002-22-2-2-2222-2-200000000002i−2i2i−2i0000-2-22200002-22-200000000-2-222-2-2220000−2i2i2i−2i2i−2i00000000−2i2i−2i2i000000000000
χ4722-2-2-22200002-22-2-2-2222-2-20000000000−2i2i−2i2i000022-2-200002-22-20000000022-2-222-2-20000−2i2i−2i2i−2i2i00000000−2i2i−2i2i000000000000
χ4822-2-2-22200002-22-2-2-2222-2-20000000000−2i2i−2i2i0000-2-22200002-22-200000000-2-222-2-22200002i−2i−2i2i−2i2i000000002i−2i2i−2i000000000000
χ4922-2-2-2220000-22-22-2-2222-2-200000000002i−2i−2i2i22-2-200000000-22-2222-2-222-2-200000000002i−2i002i−2i−2i2i00002i−2i2i−2i0000000000000000
χ5022-2-2-2220000-22-22-2-2222-2-200000000002i−2i−2i2i-2-22200000000-22-22-2-222-2-2220000000000−2i2i002i−2i−2i2i0000−2i2i−2i2i0000000000000000
χ5122-2-2-2220000-22-22-2-2222-2-20000000000−2i2i2i−2i22-2-200000000-22-2222-2-222-2-20000000000−2i2i00−2i2i2i−2i0000−2i2i−2i2i0000000000000000
χ5222-2-2-2220000-22-22-2-2222-2-20000000000−2i2i2i−2i-2-22200000000-22-22-2-222-2-22200000000002i−2i00−2i2i2i−2i00002i−2i2i−2i0000000000000000
χ5322-2-2-22-100002-22-211-1-1-111−i3−i3i3i3−i3−i3i3i3002i−2i2i−2i000022-2-2−i3i3−i3i3-11-11−i3−i3i3i3i3i3−i3−i3-1-111-1-11100002i−2i−ii−ii3−33−33−3−33−ii−ii000000000000
χ5422-2-2-22-100002-22-211-1-1-111−i3−i3i3i3−i3−i3i3i3002i−2i2i−2i0000-2-222−i3i3−i3i3-11-11i3i3−i3−i3−i3−i3i3i311-1-111-1-10000−2i2i−ii−ii3−33−3−333−3i−ii−i000000000000
χ5522-2-2-22-100002-22-211-1-1-111−i3−i3i3i3−i3−i3i3i300−2i2i−2i2i000022-2-2−i3i3−i3i3-11-11−i3−i3i3i3i3i3−i3−i3-1-111-1-1110000−2i2ii−ii−i−33−33−333−3i−ii−i000000000000
χ5622-2-2-22-100002-22-211-1-1-111−i3−i3i3i3−i3−i3i3i300−2i2i−2i2i0000-2-222−i3i3−i3i3-11-11i3i3−i3−i3−i3−i3i3i311-1-111-1-100002i−2ii−ii−i−33−333−3−33−ii−ii000000000000
χ5722-2-2-22-100002-22-211-1-1-111i3i3−i3−i3i3i3−i3−i3002i−2i2i−2i000022-2-2i3−i3i3−i3-11-11i3i3−i3−i3−i3−i3i3i3-1-111-1-11100002i−2i−ii−ii−33−33−333−3−ii−ii000000000000
χ5822-2-2-22-100002-22-211-1-1-111i3i3−i3−i3i3i3−i3−i3002i−2i2i−2i0000-2-222i3−i3i3−i3-11-11−i3−i3i3i3i3i3−i3−i311-1-111-1-10000−2i2i−ii−ii−33−333−3−33i−ii−i000000000000
χ5922-2-2-22-100002-22-211-1-1-111i3i3−i3−i3i3i3−i3−i300−2i2i−2i2i000022-2-2i3−i3i3−i3-11-11i3i3−i3−i3−i3−i3i3i3-1-111-1-1110000−2i2ii−ii−i3−33−33−3−33i−ii−i000000000000
χ6022-2-2-22-100002-22-211-1-1-111i3i3−i3−i3i3i3−i3−i300−2i2i−2i2i0000-2-222i3−i3i3−i3-11-11−i3−i3i3i3i3i3−i3−i311-1-111-1-100002i−2ii−ii−i3−33−3−333−3−ii−ii000000000000
χ6122-2-2-22-10000-22-2211-1-1-111−i3−i3i3i3−i3−i3i3i3002i−2i−2i2i22-2-20000i3−i3i3−i31-11-1-1-111-1-111−i3−i3i3i3i3i3−i3−i3002i−2i00−iii−i3−3−33−ii−ii3−3−33000000000000
χ6222-2-2-22-10000-22-2211-1-1-111−i3−i3i3i3−i3−i3i3i3002i−2i−2i2i-2-2220000i3−i3i3−i31-11-111-1-111-1-1i3i3−i3−i3−i3−i3i3i300−2i2i00−iii−i3−3−33i−ii−i−333−3000000000000
χ6322-2-2-22-10000-22-2211-1-1-111−i3−i3i3i3−i3−i3i3i300−2i2i2i−2i22-2-20000i3−i3i3−i31-11-1-1-111-1-111−i3−i3i3i3i3i3−i3−i300−2i2i00i−i−ii−333−3i−ii−i−333−3000000000000
χ6422-2-2-22-10000-22-2211-1-1-111−i3−i3i3i3−i3−i3i3i300−2i2i2i−2i-2-2220000i3−i3i3−i31-11-111-1-111-1-1i3i3−i3−i3−i3−i3i3i3002i−2i00i−i−ii−333−3−ii−ii3−3−33000000000000
χ6522-2-2-22-10000-22-2211-1-1-111i3i3−i3−i3i3i3−i3−i3002i−2i−2i2i22-2-20000−i3i3−i3i31-11-1-1-111-1-111i3i3−i3−i3−i3−i3i3i3002i−2i00−iii−i−333−3−ii−ii−333−3000000000000
χ6622-2-2-22-10000-22-2211-1-1-111i3i3−i3−i3i3i3−i3−i3002i−2i−2i2i-2-2220000−i3i3−i3i31-11-111-1-111-1-1−i3−i3i3i3i3i3−i3−i300−2i2i00−iii−i−333−3i−ii−i3−3−33000000000000
χ6722-2-2-22-10000-22-2211-1-1-111i3i3−i3−i3i3i3−i3−i300−2i2i2i−2i22-2-20000−i3i3−i3i31-11-1-1-111-1-111i3i3−i3−i3−i3−i3i3i300−2i2i00i−i−ii3−3−33i−ii−i3−3−33000000000000
χ6822-2-2-22-10000-22-2211-1-1-111i3i3−i3−i3i3i3−i3−i300−2i2i2i−2i-2-2220000−i3i3−i3i31-11-111-1-111-1-1−i3−i3i3i3i3i3−i3−i3002i−2i00i−i−ii3−3−33−ii−ii−333−3000000000000
χ694444-4-4-244-4-444-4-422-222-2-2-2-2-2-222224-4000000000000-2-222-2-22200000000000000000000000000000000000000000000000000
χ704444-4-4-244-4-4-4-44422-222-2-2-2-2-2-22222-4400000000000022-2-222-2-200000000000000000000000000000000000000000000000000
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χ7644-4-44-4-200004-4-44-2-2-222222i32i3−2i3−2i3−2i3−2i32i32i3000000000000002i3−2i3−2i32i3-222-200000000000000000000000000000000000000000000000000
χ7744-4-44-4-20000-444-4-2-2-22222−2i3−2i32i32i32i32i3−2i3−2i3000000000000002i3−2i3−2i32i32-2-2200000000000000000000000000000000000000000000000000
χ7844-4-44-4-20000-444-4-2-2-222222i32i3−2i3−2i3−2i3−2i32i32i300000000000000−2i32i32i3−2i32-2-2200000000000000000000000000000000000000000000000000
χ794-44-4004004i−4i000000-4004-400004i−4i4i−4i0000002-22-22i−2i2i−2i000000002-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ804-44-4004004i−4i000000-4004-400004i−4i4i−4i000000-22-22−2i2i−2i2i00000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ814-44-400400−4i4i000000-4004-40000−4i4i−4i4i0000002-22-2−2i2i−2i2i000000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
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χ874-44-400-200−4i4i0000−2i32i32−2i32i3-22−2323−23232i−2i2i−2i0000002-22-2−2i2i−2i2i00000000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000000000000000000000000000000000
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χ934-4-44004−4i4i00000000-400-44−4i4i4i−4i00000000002-2-22−2i2i2i−2i000000002-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ944-4-44004−4i4i00000000-400-44−4i4i4i−4i0000000000-222-22i−2i−2i2i00000000-222-2-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ954-4-4400-24i−4i000000−2i32i322i3−2i32-2−2i2i2i−2i−232323−230000002-2-222i−2i−2i2i00000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i32ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000000000000000
χ964-4-4400-24i−4i000000−2i32i322i3−2i32-2−2i2i2i−2i−232323−23000000-222-2−2i2i2i−2i000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000000000000000
χ974-4-4400-24i−4i0000002i3−2i32−2i32i32-2−2i2i2i−2i23−23−23230000002-2-222i−2i−2i2i00000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i32ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000000000000000
χ984-4-4400-24i−4i0000002i3−2i32−2i32i32-2−2i2i2i−2i23−23−2323000000-222-2−2i2i2i−2i000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000000000000000
χ994-4-4400-2−4i4i000000−2i32i322i3−2i32-22i−2i−2i2i23−23−23230000002-2-22−2i2i2i−2i00000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000000000000000000000
χ1004-4-4400-2−4i4i000000−2i32i322i3−2i32-22i−2i−2i2i23−23−2323000000-222-22i−2i−2i2i000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i32ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000000000000000000000
χ1014-4-4400-2−4i4i0000002i3−2i32−2i32i32-22i−2i−2i2i−232323−230000002-2-22−2i2i2i−2i00000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000000000000000000000
χ1024-4-4400-2−4i4i0000002i3−2i32−2i32i32-22i−2i−2i2i−232323−23000000-222-22i−2i−2i2i000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i32ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.