Finite Group Databasebeta

← Group #10697961

Character table — Group #10697961

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344444444444466666668888888812121212121212121212121224242424242424242424242424242424888888888888888822446666121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ922222222222-2-2-2-222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1022222222222-2-2-2-222-2-2-2-22222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ11222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ12222222222-2-222-2-2-2-222-2-2222222200000000-2-22222-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ13222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-20000000000000000000000002222-2-2-2-20000000000000000
χ14222222222-2-2-2-222-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-2-2-222220000000000000000
χ1522222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ1622222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ1722222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ1822222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ1922222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000−i3−i3i3i3−i3−i3i3i30000
χ2022222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111100000000000000000000i3i3−i3−i3i3i3−i3−i30000
χ2122222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3−i3i3i3i3i3−i3−i30000
χ2222222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3i3−i3−i3−i3−i3i3i30000
χ23222-22-2-2-22002-200002-20022-22-2-2-2−i2−i2i2i2−i2−i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000022-2-2−i2−i2i2i2−i2−i2i2i20000000000000000
χ24222-22-2-2-22002-200002-20022-22-2-2-2−i2−i2i2i2−i2−i2i2i20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000-2-222i2i2−i2−i2i2i2−i2−i20000000000000000
χ25222-22-2-2-22002-200002-20022-22-2-2-2i2i2−i2−i2i2i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i20000000000000000
χ26222-22-2-2-22002-200002-20022-22-2-2-2i2i2−i2−i2i2i2−i2−i20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-2-222−i2−i2i2i2−i2−i2i2i20000000000000000
χ27222-22-2-2-2200-220000-220022-22-2-2-2−i2−i2i2i2i2i2−i2−i200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i222-2-20000−i2−i2i2i2i2i2−i2−i20000000000000000
χ28222-22-2-2-2200-220000-220022-22-2-2-2−i2−i2i2i2i2i2−i2−i200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i20000000000000000
χ29222-22-2-2-2200-220000-220022-22-2-2-2i2i2−i2−i2−i2−i2i2i200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i222-2-20000i2i2−i2−i2−i2−i2i2i20000000000000000
χ30222-22-2-2-2200-220000-220022-22-2-2-2i2i2−i2−i2−i2−i2i2i200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-2220000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3122-22-22-2-222-200002-200002-22-22-2-200002i−2i2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-22-2-222-200002-200002-22-22-2-200002i−2i2i−2i2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-22-2-222-200002-200002-22-22-2-20000−2i2i−2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-22-22-2-222-200002-200002-22-22-2-20000−2i2i−2i2i2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-22-22-2-22-220000-2200002-22-22-2-22i−2i2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i000000002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ3622-22-22-2-22-220000-2200002-22-22-2-22i−2i2i−2i0000-2200000000-222i2i−2i−2i2i2i−2i−2i00000000−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ3722-22-22-2-22-220000-2200002-22-22-2-2−2i2i−2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ3822-22-22-2-22-220000-2200002-22-22-2-2−2i2i−2i2i0000-2200000000-22−2i−2i2i2i−2i−2i2i2i00000000−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ3922-2-2-2-222200002-200002-22-2-2-2-2222−2−222−2−2200000022-2-20022−2−2−2−22222−2−2−2−2222−2−222−2−220000-222-20000000000000000
χ4022-2-2-2-222200002-200002-22-2-2-2-2222−2−222−2−2200000022-2-20022−2−2−2−22222−2−2−2−222−222−2−222−200002-2-220000000000000000
χ4122-2-2-2-222200002-200002-22-2-2-2-222−222−2−222−200000022-2-200−2−22222−2−2−2−22222−2−22−2−222−2−2200002-2-220000000000000000
χ4222-2-2-2-222200002-200002-22-2-2-2-222−222−2−222−200000022-2-200−2−22222−2−2−2−22222−2−2−222−2−222−20000-222-20000000000000000
χ4322-2-2-2-22220000-220000-222-2-2-2-2222−2−22−222−2000000-2-2220022−2−2−2−222−2−22222−2−22−2−22−222−2-222-200000000000000000000
χ4422-2-2-2-22220000-220000-222-2-2-2-2222−2−22−222−2000000-2-2220022−2−2−2−222−2−22222−2−2−222−22−2−222-2-2200000000000000000000
χ4522-2-2-2-22220000-220000-222-2-2-2-222−222−22−2−22000000-2-22200−2−22222−2−222−2−2−2−2222−2−22−222−22-2-2200000000000000000000
χ4622-2-2-2-22220000-220000-222-2-2-2-222−222−22−2−22000000-2-22200−2−22222−2−222−2−2−2−222−222−22−2−22-222-200000000000000000000
χ472-2-2-222-222222222-2-2-2-2-2-2-2-2-2222-200000000222-22-22-22-2-2-200000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ482-2-2-222-222222222-2-2-2-2-2-2-2-2-2222-200000000222-22-22-22-2-2-20000000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ492-2-2-222-22222-2-2-2-2-2-22222-2-2-2222-20000000022-22-22-22-22-2-2000000000000000000000000000000002-2002-22-200000000
χ502-2-2-222-22222-2-2-2-2-2-22222-2-2-2222-20000000022-22-22-22-22-2-200000000000000000000000000000000-2200-22-2200000000
χ512-2-2-222-222-2-222-2-222-2-222-2-2-2222-200000000-2-22-22-2-22-222200000000000000000000000000000000000000000000002-2
χ522-2-2-222-222-2-222-2-222-2-222-2-2-2222-200000000-2-22-22-2-22-22220000000000000000000000000000000000000000000000-22
χ532-2-2-222-222-2-2-2-2222222-2-2-2-2-2222-200000000-2-2-22-222-22-222000000000000000000000000000000000000000000002-200
χ542-2-2-222-222-2-2-2-2222222-2-2-2-2-2222-200000000-2-2-22-222-22-22200000000000000000000000000000000000000000000-2200
χ552-2-2-222-22-1222222-2-2-2-2-2-2111-1-1-1100000000-1-1-11-11-11-11113−33−33−33−33−33−33−33−30000000000000000002i−2i−i3i3i3−i3−ii−ii0000
χ562-2-2-222-22-1222222-2-2-2-2-2-2111-1-1-1100000000-1-1-11-11-11-11113−33−33−33−33−33−33−33−3000000000000000000−2i2ii3−i3−i3i3i−ii−i0000
χ572-2-2-222-22-1222222-2-2-2-2-2-2111-1-1-1100000000-1-1-11-11-11-1111−33−33−33−33−33−33−33−330000000000000000002i−2ii3−i3−i3i3−ii−ii0000
χ582-2-2-222-22-1222222-2-2-2-2-2-2111-1-1-1100000000-1-1-11-11-11-1111−33−33−33−33−33−33−33−33000000000000000000−2i2i−i3i3i3−i3i−ii−i0000
χ592-2-2-222-22-122-2-2-2-2-2-22222111-1-1-1100000000-1-11-11-11-11-1113−33−33−33−3−33−33−33−3300000000000000002-200-11-113−3−330000
χ602-2-2-222-22-122-2-2-2-2-2-22222111-1-1-1100000000-1-11-11-11-11-1113−33−33−33−3−33−33−33−330000000000000000-22001-11-1−333−30000
χ612-2-2-222-22-122-2-2-2-2-2-22222111-1-1-1100000000-1-11-11-11-11-111−33−33−33−333−33−33−33−300000000000000002-200-11-11−333−30000
χ622-2-2-222-22-122-2-2-2-2-2-22222111-1-1-1100000000-1-11-11-11-11-111−33−33−33−333−33−33−33−30000000000000000-22001-11-13−3−330000
χ6344444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-20000000022-2-2-2-2222222000000000000000000000000000000000000000000000000
χ6444444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-200000000222222-2-2-2-222000000000000000000000000000000000000000000000000
χ65444-44-4-4-4-2004-400004-400-2-22-2222−2i2−2i22i22i2−2i2−2i22i22i200-2-222000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000000000000000000000000000
χ66444-44-4-4-4-2004-400004-400-2-22-22222i22i2−2i2−2i22i22i2−2i2−2i200-2-222000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000000000000000000000
χ67444-44-4-4-4-200-440000-4400-2-22-2222−2i2−2i22i22i22i22i2−2i2−2i20022-2-2000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200000000000000000000000000000000
χ68444-44-4-4-4-200-440000-4400-2-22-22222i22i2−2i2−2i2−2i2−2i22i22i20022-2-2000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200000000000000000000000000000000
χ6944-44-44-4-4-24-400004-40000-22-22-22200004i−4i4i−4i-2200000000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ7044-44-44-4-4-24-400004-40000-22-22-2220000−4i4i−4i4i-2200000000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ7144-44-44-4-4-2-440000-440000-22-22-2224i−4i4i−4i00002-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ7244-44-44-4-4-2-440000-440000-22-22-222−4i4i−4i4i00002-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ7344-4-4-4-444-200004-400004-4-22222-2-222−22−222222−22−2222000000-2-22200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7444-4-4-4-444-200004-400004-4-22222-2-2−222222−22−222222−22000000-2-2220022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ7544-4-4-4-444-20000-440000-44-22222-2-222−22−2222−222222−2200000022-2-200−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ7644-4-4-4-444-20000-440000-44-22222-2-2−222222−2222−22−222200000022-2-20022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ774-444-4-4-44400004-40000-44-444-4-44-4000000000000004-4-4400000000000000000000000000000000000000000000000000
χ784-444-4-4-4440000-4400004-4-444-4-44-400000000000000-444-400000000000000000000000000000000000000000000000000
χ794-444-4-4-44-200004-40000-442-2-222-2200000000000000-222-2006−6−66−666−66−6−66−666−600000000000000000000000000000000
χ804-444-4-4-44-200004-40000-442-2-222-2200000000000000-222-200−666−66−6−66−666−66−6−6600000000000000000000000000000000
χ814-444-4-4-44-20000-4400004-42-2-222-22000000000000002-2-22006−6−66−666−6−666−66−6−6600000000000000000000000000000000
χ824-444-4-4-44-20000-4400004-42-2-222-22000000000000002-2-2200−666−66−6−666−6−66−666−600000000000000000000000000000000
χ834-44-4-444-444-40000-440000-44-4-44-44000000004-400000000-44000000000000000000000000000000000000000000000000
χ844-44-4-444-44-4400004-40000-44-4-44-4400000000-44000000004-4000000000000000000000000000000000000000000000000
χ854-44-4-444-4-24-40000-4400002-222-22-200000000-22000000002-200000000−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000
χ864-44-4-444-4-24-40000-4400002-222-22-200000000-22000000002-2000000002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000
χ874-44-4-444-4-2-4400004-400002-222-22-2000000002-200000000-22−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ884-44-4-444-4-2-4400004-400002-222-22-2000000002-200000000-222i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ894-4-444-44-44004-40000-4400-4-444-4-4400000000004-4-44000000000000000000000000000000000000000000000000000000
χ904-4-444-44-4400-4400004-400-4-444-4-440000000000-444-4000000000000000000000000000000000000000000000000000000
χ914-4-444-44-4-2004-40000-440022-2-222-20000000000-222-2000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ924-4-444-44-4-2004-40000-440022-2-222-20000000000-222-2000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ934-4-444-44-4-200-4400004-40022-2-222-200000000002-2-22000000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ944-4-444-44-4-200-4400004-40022-2-222-200000000002-2-22000000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ954-4-4-444-44-2-4-444-4-444-4-444222-2-2-220000000022-22-222-22-2-2-2000000000000000000000000000000000000000000000000
χ964-4-4-444-44-2-4-4-4-4444444-4-4222-2-2-2200000000222-22-2-22-22-2-2000000000000000000000000000000000000000000000000

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