Finite Group Databasebeta

← Group #10706391

Character table — Group #10706391

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222222222444444444444444444161616161616242424242424242411222222222224444444444444444441616161616162424242424242424
order12234466688884488121212121212242424242424242422666616161616161616162226446668888448812121212121224242424242424242266661616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1ii−i−iii−i−i111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1ii−i−iii−i−i
χ6111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1−i−iii−i−iii111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1−i−iii−i−iii
χ7111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111ii−i−i−i−iii111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111ii−i−i−i−iii
χ8111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111−i−iiiii−i−i111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111−i−iiiii−i−i
χ922222222222-2-2-2-22-2-2-2-2-2222222-2-2-2-20000000000000022222222222-2-2-2-22-2-2-2-2-2222222-2-2-2-200000000000000
χ10222222222-2-222-2-2-22-2-2-2-222-2-2-2-2222200000000000000222222222-2-222-2-2-22-2-2-2-222-2-2-2-2222200000000000000
χ11222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ12222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100000000222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100000000
χ13222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100−i3i3−i3i300000000222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100−i3i3−i3i300000000
χ14222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100i3−i3i3−i300000000222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100i3−i3i3−i300000000
χ15222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100−i3i3i3−i300000000222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100−i3i3i3−i300000000
χ16222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100i3−i3−i3i300000000222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100i3−i3−i3i300000000
χ17222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1111111112-2-1-11100000000222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1111111112-2-1-11100000000
χ18222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-111111111-2211-1-100000000222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-111111111-2211-1-100000000
χ1922-222-22-2-20022000-200002-2000022-2-20000002−22−2000022-222-22-2-20022000-200002-2000022-2-20000002−22−20000
χ2022-222-22-2-20022000-200002-2000022-2-2000000−22−22000022-222-22-2-20022000-200002-2000022-2-2000000−22−220000
χ2122-222-22-2-200-2-2000200002-20000-2-222000000−i2i2i2−i2000022-222-22-2-200-2-2000200002-20000-2-222000000−i2i2i2−i20000
χ2222-222-22-2-200-2-2000200002-20000-2-222000000i2−i2−i2i2000022-222-22-2-200-2-2000200002-20000-2-222000000i2−i2−i2i20000
χ2322-22-222-2-2220000-200000-2222-2-2000000000000002−22−222-22-222-2-2220000-200000-2222-2-2000000000000002−22−2
χ2422-22-222-2-2220000-200000-2222-2-200000000000000−22−2222-22-222-2-2220000-200000-2222-2-200000000000000−22−22
χ2522-22-222-2-2-2-20000200000-22-2-22200000000000000−i2i2i2−i222-22-222-2-2-2-20000200000-22-2-22200000000000000−i2i2i2−i2
χ2622-22-222-2-2-2-20000200000-22-2-22200000000000000i2−i2−i2i222-22-222-2-2-2-20000200000-22-2-22200000000000000i2−i2−i2i2
χ274444-4-4444000000000000-4-400000000000000000000004444-4-4444000000000000-4-40000000000000000000000
χ28444-2-4-4-2-2-200000000−2i3−2i32i32i3220000000000000000000000444-2-4-4-2-2-200000000−2i3−2i32i32i3220000000000000000000000
χ29444-2-4-4-2-2-2000000002i32i3−2i3−2i3220000000000000000000000444-2-4-4-2-2-2000000002i32i3−2i3−2i3220000000000000000000000
χ3044-4-24-4-2220044000-40000-220000-2-2220000000000000044-4-24-4-2220044000-40000-220000-2-22200000000000000
χ3144-4-24-4-22200-4-400040000-22000022-2-20000000000000044-4-24-4-22200-4-400040000-22000022-2-200000000000000
χ3244-4-2-44-222440000-4000002-2-2-22200000000000000000044-4-2-44-222440000-4000002-2-2-222000000000000000000
χ3344-4-2-44-222-4-400004000002-222-2-200000000000000000044-4-2-44-222-4-400004000002-222-2-2000000000000000000
χ344-40400-40022−2222−222-2002-22-20022−220022−2200000000000000004-40400-40022−2222−222-2002-22-20022−220022−220000000000000000
χ354-40400-40022−22−2222-2200-22-220022−2200−222200000000000000004-40400-40022−22−2222-2200-22-220022−2200−22220000000000000000
χ364-40400-400−222222−22-2200-22-2200−22220022−2200000000000000004-40400-400−222222−22-2200-22-2200−22220022−220000000000000000
χ374-40400-400−2222−22222-2002-22-200−222200−222200000000000000004-40400-400−2222−22222-2002-22-200−222200−22220000000000000000
χ384-40-2002−2i32i322−2222−222-200−1−i31+i3−1+i31−i300−22i6−i6−22i6−i6000000000000004-40-2002−2i32i322−2222−222-200−1−i31+i3−1+i31−i300−22i6−i6−22i6−i600000000000000
χ394-40-2002−2i32i322−22−2222-22001+i3−1−i31−i3−1+i300−22i6−i62−2−i6i6000000000000004-40-2002−2i32i322−22−2222-22001+i3−1−i31−i3−1+i300−22i6−i62−2−i6i600000000000000
χ404-40-2002−2i32i3−222222−22-22001+i3−1−i31−i3−1+i3002−2−i6i6−22i6−i6000000000000004-40-2002−2i32i3−222222−22-22001+i3−1−i31−i3−1+i3002−2−i6i6−22i6−i600000000000000
χ414-40-2002−2i32i3−2222−22222-200−1−i31+i3−1+i31−i3002−2−i6i62−2−i6i6000000000000004-40-2002−2i32i3−2222−22222-200−1−i31+i3−1+i31−i3002−2−i6i62−2−i6i600000000000000
χ424-40-20022i3−2i322−2222−222-200−1+i31−i3−1−i31+i300−22−i6i6−22−i6i6000000000000004-40-20022i3−2i322−2222−222-200−1+i31−i3−1−i31+i300−22−i6i6−22−i6i600000000000000
χ434-40-20022i3−2i322−22−2222-22001−i3−1+i31+i3−1−i300−22−i6i62−2i6−i6000000000000004-40-20022i3−2i322−22−2222-22001−i3−1+i31+i3−1−i300−22−i6i62−2i6−i600000000000000
χ444-40-20022i3−2i3−222222−22-22001−i3−1+i31+i3−1−i3002−2i6−i6−22−i6i6000000000000004-40-20022i3−2i3−222222−22-22001−i3−1+i31+i3−1−i3002−2i6−i6−22−i6i600000000000000
χ454-40-20022i3−2i3−2222−22222-200−1+i31−i3−1−i31+i3002−2i6−i62−2i6−i6000000000000004-40-20022i3−2i3−2222−22222-200−1+i31−i3−1−i31+i3002−2i6−i62−2i6−i600000000000000
χ46111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ471111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ481111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ491111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ50111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-11-1-111−i−iii−i−iii
χ51111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-111-1-1−i−iii−i−iii-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-11-1-111ii−i−iii−i−i
χ52111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111ii−i−i−i−iii-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111111-111-1-1−i−iiiii−i−i
χ53111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-111−i−iiiii−i−i-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111111-111-1-1ii−i−i−i−iii
χ5422222222222-2-2-2-22-2-2-2-2-2222222-2-2-2-200000000000000-2-2-2-2-2-2-2-2-2-2-22222-222222-2-2-2-2-2-2222200000000000000
χ55222222222-2-222-2-2-22-2-2-2-222-2-2-2-2222200000000000000-2-2-2-2-2-2-2-2-222-2-2222-22222-2-22222-2-2-2-200000000000000
χ56222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000-2-2-21-2-2111-2-2-2-2-2-2-2-211111111111111-2-2111100000000
χ57222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100000000-2-2-21-2-2111-2-2-2-2-2-2-2-21111111111111122-1-1-1-100000000
χ58222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100−i3i3−i3i300000000-2-2-21-2-2111-2-22222-22-1-1-1-1111111-1-1-1-100i3−i3i3−i300000000
χ59222-122-1-1-122-2-2-2-22-21111-1-1-1-1-1-1111100i3−i3i3−i300000000-2-2-21-2-2111-2-22222-22-1-1-1-1111111-1-1-1-100−i3i3−i3i300000000
χ60222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100−i3i3i3−i300000000-2-2-21-2-211122-2-2222-2-1-1-1-111-1-1-1-1111100i3−i3−i3i300000000
χ61222-122-1-1-1-2-222-2-2-221111-1-11111-1-1-1-100i3−i3−i3i300000000-2-2-21-2-211122-2-2222-2-1-1-1-111-1-1-1-1111100−i3i3i3−i300000000
χ62222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1111111112-2-1-11100000000-2-2-21-2-21112222-2-222111111-1-1-1-1-1-1-1-1-2211-1-100000000
χ63222-122-1-1-1-2-2-2-222-2-2-1-1-1-1-1-111111111-2211-1-100000000-2-2-21-2-21112222-2-222111111-1-1-1-1-1-1-1-12-2-1-11100000000
χ6422-222-22-2-20022000-200002-2000022-2-20000002−22−20000-2-22-2-22-22200-2-200020000-220000-2-222000000−22−220000
χ6522-222-22-2-20022000-200002-2000022-2-2000000−22−220000-2-22-2-22-22200-2-200020000-220000-2-2220000002−22−20000
χ6622-222-22-2-200-2-2000200002-20000-2-222000000−i2i2i2−i20000-2-22-2-22-2220022000-20000-22000022-2-2000000i2−i2−i2i20000
χ6722-222-22-2-200-2-2000200002-20000-2-222000000i2−i2−i2i20000-2-22-2-22-2220022000-20000-22000022-2-2000000−i2i2i2−i20000
χ6822-22-222-2-2220000-200000-2222-2-2000000000000002−22−2-2-22-22-2-222-2-200002000002-2-2-22200000000000000−22−22
χ6922-22-222-2-2220000-200000-2222-2-200000000000000−22−22-2-22-22-2-222-2-200002000002-2-2-222000000000000002−22−2
χ7022-22-222-2-2-2-20000200000-22-2-22200000000000000−i2i2i2−i2-2-22-22-2-222220000-2000002-222-2-200000000000000i2−i2−i2i2
χ7122-22-222-2-2-2-20000200000-22-2-22200000000000000i2−i2−i2i2-2-22-22-2-222220000-2000002-222-2-200000000000000−i2i2i2−i2
χ724444-4-4444000000000000-4-40000000000000000000000-4-4-4-444-4-4-4000000000000440000000000000000000000
χ73444-2-4-4-2-2-200000000−2i3−2i32i32i3220000000000000000000000-4-4-4244222000000002i32i3−2i3−2i3-2-20000000000000000000000
χ74444-2-4-4-2-2-2000000002i32i3−2i3−2i3220000000000000000000000-4-4-424422200000000−2i3−2i32i32i3-2-20000000000000000000000
χ7544-4-24-4-2220044000-40000-220000-2-22200000000000000-4-442-442-2-200-4-4000400002-2000022-2-200000000000000
χ7644-4-24-4-22200-4-400040000-22000022-2-200000000000000-4-442-442-2-20044000-400002-20000-2-22200000000000000
χ7744-4-2-44-222440000-4000002-2-2-222000000000000000000-4-4424-42-2-2-4-40000400000-2222-2-2000000000000000000
χ7844-4-2-44-222-4-400004000002-222-2-2000000000000000000-4-4424-42-2-2440000-400000-22-2-222000000000000000000
χ794-40400-40022−2222−222-2002-22-20022−220022−220000000000000000-440-400400−2222−2222-2200-22-2200−222200−22220000000000000000
χ804-40400-40022−22−2222-2200-22-220022−2200−22220000000000000000-440-400400−222222−222-2002-22-200−22220022−220000000000000000
χ814-40400-400−222222−22-2200-22-2200−22220022−220000000000000000-440-40040022−22−22222-2002-22-20022−2200−22220000000000000000
χ824-40400-400−2222−22222-2002-22-200−222200−22220000000000000000-440-40040022−2222−22-2200-22-220022−220022−220000000000000000
χ834-40-2002−2i32i322−2222−222-200−1−i31+i3−1+i31−i300−22i6−i6−22i6−i600000000000000-440200-22i3−2i3−2222−2222-22001+i3−1−i31−i3−1+i3002−2−i6i62−2−i6i600000000000000
χ844-40-2002−2i32i322−22−2222-22001+i3−1−i31−i3−1+i300−22i6−i62−2−i6i600000000000000-440200-22i3−2i3−222222−222-200−1−i31+i3−1+i31−i3002−2−i6i6−22i6−i600000000000000
χ854-40-2002−2i32i3−222222−22-22001+i3−1−i31−i3−1+i3002−2−i6i6−22i6−i600000000000000-440200-22i3−2i322−22−22222-200−1−i31+i3−1+i31−i300−22i6−i62−2−i6i600000000000000
χ864-40-2002−2i32i3−2222−22222-200−1−i31+i3−1+i31−i3002−2−i6i62−2−i6i600000000000000-440200-22i3−2i322−2222−22-22001+i3−1−i31−i3−1+i300−22i6−i6−22i6−i600000000000000
χ874-40-20022i3−2i322−2222−222-200−1+i31−i3−1−i31+i300−22−i6i6−22−i6i600000000000000-440200-2−2i32i3−2222−2222-22001−i3−1+i31+i3−1−i3002−2i6−i62−2i6−i600000000000000
χ884-40-20022i3−2i322−22−2222-22001−i3−1+i31+i3−1−i300−22−i6i62−2i6−i600000000000000-440200-2−2i32i3−222222−222-200−1+i31−i3−1−i31+i3002−2i6−i6−22−i6i600000000000000
χ894-40-20022i3−2i3−222222−22-22001−i3−1+i31+i3−1−i3002−2i6−i6−22−i6i600000000000000-440200-2−2i32i322−22−22222-200−1+i31−i3−1−i31+i300−22−i6i62−2i6−i600000000000000
χ904-40-20022i3−2i3−2222−22222-200−1+i31−i3−1−i31+i3002−2i6−i62−2i6−i600000000000000-440200-2−2i32i322−2222−22-22001−i3−1+i31+i3−1−i300−22−i6i6−22−i6i600000000000000

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