Finite Group Databasebeta

← Group #10829219

Character table — Group #10829219

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444422444444441212121212121212244444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-11111
χ9111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-111-1-1-111111-1-111-1-1
χ10111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-111-1-11-1-1-1-1-111-1-111
χ11111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-111-1-111-1-1-11-1-11111-1-1
χ12111111111-1-1-1-111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-111-1-111111-111-1-1-1-111
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-11-1-11111-1-1-1-1-111111-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-11-1-11111-1-1111-1-1-1-1-111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111111111-1-11-111-1-1-1-111-1111-1-1-1-1-1-111
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111-111-1-1-1-1111-1-1-1111111-1-1
χ172222222222222-2-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000220000220000000000-200-200000000
χ182222222222222-2-2-2-22222222-2-200000000-2-22222-2-2-2-2-2-200000000000000000000-2-20000-2-20000000000200200000000
χ19222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000220000-2-20000000000200-200000000
χ20222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000-2-20000220000000000-200200000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-21111-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000000022-1-1-1-11111000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-200000000-2211-1-1-1-111000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-2-1-11111-1-1000000000000
χ29222-2-2-2-2220000-22-22222-2-2-2-200000022-2-22-2000000002-2000000002222-2-2-2-20000002i2i−2i−2i00000000000002i−2i000000000
χ30222-2-2-2-2220000-22-22222-2-2-2-200000022-2-22-2000000002-2000000002222-2-2-2-2000000−2i−2i2i2i0000000000000−2i2i000000000
χ31222-2-2-2-2220000-22-22222-2-2-2-2000000-2-2222-2000000002-200000000-2-2-2-222220000002i2i−2i−2i0000000000000−2i2i000000000
χ32222-2-2-2-2220000-22-22222-2-2-2-2000000-2-2222-2000000002-200000000-2-2-2-22222000000−2i−2i2i2i00000000000002i−2i000000000
χ3322-22-2-22-222i2i−2i−2i00002-2-22-22-200−i2−i2i2i22−22−2002i2i−2i−2i000000−i2−i2−i2−i2i2i2i2i222−2−222−2−200002-200002i−2i000000000000000000−i2i22−2
χ3422-22-2-22-222i2i−2i−2i00002-2-22-22-200−i2−i2i2i22−22−2002i2i−2i−2i000000−i2−i2−i2−i2i2i2i2i222−2−222−2−20000-220000−2i2i000000000000000000i2−i2−22
χ3522-22-2-22-222i2i−2i−2i00002-2-22-22-200i2i2−i2−i2−22−22002i2i−2i−2i000000i2i2i2i2−i2−i2−i2−i2−2−222−2−22200002-200002i−2i000000000000000000i2−i2−22
χ3622-22-2-22-222i2i−2i−2i00002-2-22-22-200i2i2−i2−i2−22−22002i2i−2i−2i000000i2i2i2i2−i2−i2−i2−i2−2−222−2−2220000-220000−2i2i000000000000000000−i2i22−2
χ3722-22-2-22-22−2i−2i2i2i00002-2-22-22-200−i2−i2i2i2−22−2200−2i−2i2i2i000000−i2−i2−i2−i2i2i2i2i2−2−222−2−22200002-20000−2i2i000000000000000000−i2i2−22
χ3822-22-2-22-22−2i−2i2i2i00002-2-22-22-200−i2−i2i2i2−22−2200−2i−2i2i2i000000−i2−i2−i2−i2i2i2i2i2−2−222−2−2220000-2200002i−2i000000000000000000i2−i22−2
χ3922-22-2-22-22−2i−2i2i2i00002-2-22-22-200i2i2−i2−i22−22−200−2i−2i2i2i000000i2i2i2i2−i2−i2−i2−i222−2−222−2−200002-20000−2i2i000000000000000000i2−i22−2
χ4022-22-2-22-22−2i−2i2i2i00002-2-22-22-200i2i2−i2−i22−22−200−2i−2i2i2i000000i2i2i2i2−i2−i2−i2−i222−2−222−2−20000-2200002i−2i000000000000000000−i2i2−22
χ412-2-222-2-222000022-2-2-2-2222-2-2002i−2i2i−2i0000-22000000002-22i2i−2i−2i2i2i−2i−2i000000000000002i−2i2i−2i0000000000000000002-20000
χ422-2-222-2-222000022-2-2-2-2222-2-2002i−2i2i−2i0000-22000000002-22i2i−2i−2i2i2i−2i−2i00000000000000−2i2i−2i2i000000000000000000-220000
χ432-2-222-2-222000022-2-2-2-2222-2-200−2i2i−2i2i0000-22000000002-2−2i−2i2i2i−2i−2i2i2i000000000000002i−2i2i−2i000000000000000000-220000
χ442-2-222-2-222000022-2-2-2-2222-2-200−2i2i−2i2i0000-22000000002-2−2i−2i2i2i−2i−2i2i2i00000000000000−2i2i−2i2i0000000000000000002-20000
χ452-2-2-2-222222-22-22-2-22-2-22-2-2222-200000000222-22-222-2-2-2-200000000000000002-22-2000000000000002-22-2000000000000
χ462-2-2-2-222222-22-22-2-22-2-22-2-2222-200000000222-22-222-2-2-2-20000000000000000-22-2200000000000000-22-22000000000000
χ472-2-2-2-222222-22-2-222-2-2-22-2-222-2200000000-2-22-22-2-2-2222200000000000000000000002-2-2200000000000000002-2000000
χ482-2-2-2-222222-22-2-222-2-2-22-2-222-2200000000-2-22-22-2-2-222220000000000000000000000-222-20000000000000000-22000000
χ492-2-2-2-22222-22-222-2-22-2-22-2-222-220000000022-22-22-2-222-2-200000000000000002-2-22000000000000002-2-22000000000000
χ502-2-2-2-22222-22-222-2-22-2-22-2-222-220000000022-22-22-2-222-2-20000000000000000-222-200000000000000-222-2000000000000
χ512-2-2-2-22222-22-22-222-2-2-22-2-2222-200000000-2-2-22-2222-2-22200000000000000000000002-2-220000000000000000-22000000
χ522-2-2-2-22222-22-22-222-2-2-22-2-2222-200000000-2-2-22-2222-2-2220000000000000000000000-222-200000000000000002-2000000
χ532-2-2-2-2222-12-22-22-2-2211-111-1-12-200000000-1-1-11-11-1-111113−33−33−33−33−33−33−33−32-22-200000000003−33−3-11-11000000000000
χ542-2-2-2-2222-12-22-22-2-2211-111-1-12-200000000-1-1-11-11-1-111113−33−33−33−33−33−33−33−3-22-220000000000−33−331-11-1000000000000
χ552-2-2-2-2222-12-22-22-2-2211-111-1-12-200000000-1-1-11-11-1-11111−33−33−33−33−33−33−33−332-22-20000000000−33−33-11-11000000000000
χ562-2-2-2-2222-12-22-22-2-2211-111-1-12-200000000-1-1-11-11-1-11111−33−33−33−33−33−33−33−33-22-2200000000003−33−31-11-1000000000000
χ572-2-2-2-2222-1-22-222-2-2211-111-1-1-2200000000-1-11-11-111-1-1113−33−33−33−3−33−33−33−332-2-2200000000003−3−33-111-1000000000000
χ582-2-2-2-2222-1-22-222-2-2211-111-1-1-2200000000-1-11-11-111-1-1113−33−33−33−3−33−33−33−33-222-20000000000−333−31-1-11000000000000
χ592-2-2-2-2222-1-22-222-2-2211-111-1-1-2200000000-1-11-11-111-1-111−33−33−33−333−33−33−33−32-2-220000000000−333−3-111-1000000000000
χ602-2-2-2-2222-1-22-222-2-2211-111-1-1-2200000000-1-11-11-111-1-111−33−33−33−333−33−33−33−3-222-200000000003−3−331-1-11000000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-40000000022-2-2-2-222222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ63444-4-4-4-44400004-44-4444-4-4-4-40000000000-4400000000-4400000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-200004-44-4-2-2-2222200000000002-2000000002-2−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000
χ65444-4-4-4-44-200004-44-4-2-2-2222200000000002-2000000002-22i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000
χ66444-4-4-4-44-20000-44-44-2-2-2222200000044-4-4-2200000000-2200000000-2-2-2-222220000000000000000000000000000000000
χ67444-4-4-4-44-20000-44-44-2-2-22222000000-4-444-2200000000-22000000002222-2-2-2-20000000000000000000000000000000000
χ6844-44-4-44-4-24i4i−4i−4i0000-222-22-2200−2i2−2i22i22i222−2222−2200−2i−2i2i2i000000i2i2i2i2−i2−i2−i2−i2−2−222−2−2220000000000000000000000000000000000
χ6944-44-4-44-4-24i4i−4i−4i0000-222-22-22002i22i2−2i2−2i2−2222−222200−2i−2i2i2i000000−i2−i2−i2−i2i2i2i2i222−2−222−2−20000000000000000000000000000000000
χ7044-44-4-44-4-2−4i−4i4i4i0000-222-22-2200−2i2−2i22i22i2−2222−2222002i2i−2i−2i000000i2i2i2i2−i2−i2−i2−i222−2−222−2−20000000000000000000000000000000000
χ7144-44-4-44-4-2−4i−4i4i4i0000-222-22-22002i22i2−2i2−2i222−2222−22002i2i−2i−2i000000−i2−i2−i2−i2i2i2i2i2−2−222−2−2220000000000000000000000000000000000
χ7244-4-444-4-44000000004-4-4-44-4400000022−22−2222000000000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ7344-4-444-4-44000000004-4-4-44-44000000−222222−2200000000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ7444-4-444-4-4-200000000-2222-22-200000022−22−222200000023−2323−23006−6−66−666−6−2−22222−2−20000000000000000000000000000000000
χ7544-4-444-4-4-200000000-2222-22-200000022−22−2222000000−2323−232300−666−66−6−66−2−22222−2−20000000000000000000000000000000000
χ7644-4-444-4-4-200000000-2222-22-2000000−222222−2200000023−2323−2300−666−66−6−6622−2−2−2−2220000000000000000000000000000000000
χ7744-4-444-4-4-200000000-2222-22-2000000−222222−22000000−2323−2323006−6−66−666−622−2−2−2−2220000000000000000000000000000000000
χ784-444-44-4-4400000000-44-44-4-440022−22−222200000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ794-444-44-4-4400000000-44-44-4-4400−222222−220000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ804-444-44-4-4-2000000002-22-222-20022−22−2222000000000023−23−232300−2−22222−2−2−666−66−6−660000000000000000000000000000000000
χ814-444-44-4-4-2000000002-22-222-20022−22−22220000000000−232323−2300−2−22222−2−26−6−66−666−60000000000000000000000000000000000
χ824-444-44-4-4-2000000002-22-222-200−222222−22000000000023−23−23230022−2−2−2−2226−6−66−666−60000000000000000000000000000000000
χ834-444-44-4-4-2000000002-22-222-200−222222−220000000000−232323−230022−2−2−2−222−666−66−6−660000000000000000000000000000000000
χ844-44-44-44-444i−4i−4i4i0000-44-4-444-40000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ854-44-44-44-44−4i4i4i−4i0000-44-4-444-4000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ864-44-44-44-4-24i−4i−4i4i00002-222-2-22000000000000−2i2i2i−2i000000i6−i6i6−i6−i6i6−i6i6−666−6−666−60000000000000000000000000000000000
χ874-44-44-44-4-24i−4i−4i4i00002-222-2-22000000000000−2i2i2i−2i000000−i6i6−i6i6i6−i6i6−i66−6−666−6−660000000000000000000000000000000000
χ884-44-44-44-4-2−4i4i4i−4i00002-222-2-220000000000002i−2i−2i2i000000i6−i6i6−i6−i6i6−i6i66−6−666−6−660000000000000000000000000000000000
χ894-44-44-44-4-2−4i4i4i−4i00002-222-2-220000000000002i−2i−2i2i000000−i6i6−i6i6i6−i6i6−i6−666−6−666−60000000000000000000000000000000000
χ904-4-444-4-4440000-4-444-4-4444-4-400000000004-400000000-4400000000000000000000000000000000000000000000000000
χ914-4-444-4-44-2000044-4-422-2-2-222004i−4i4i−4i00002-200000000-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000
χ924-4-444-4-44-2000044-4-422-2-2-22200−4i4i−4i4i00002-200000000-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000
χ934-4-444-4-44-20000-4-44422-2-2-2220000000000-22000000002-20000000023−2323−23−2323−23230000000000000000000000000000000000
χ944-4-444-4-44-20000-4-44422-2-2-2220000000000-22000000002-200000000−2323−232323−2323−230000000000000000000000000000000000
χ954-4-4-4-4444-24-44-4-444-422-222-2-2-440000000022-22-2222-2-2-2-200000000000000000000000000000000000000000000000000
χ964-4-4-4-4444-2-44-44-444-422-222-2-24-400000000222-22-2-2-222-2-200000000000000000000000000000000000000000000000000

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