Finite Group Databasebeta

← Group #125575

Character table — Group #125575

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-2220000000022-2-222-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-2220000000022-2-222-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-22200000000-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-2-2-22200000000-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-2-22222-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-22222-2-222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ29222-2-2-2-222i−2i2-22-22i−2i2i2i2i2i−2i−2i−2i−2i002i−2i00000022-2-200000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ30222-2-2-2-222i−2i2-22-22i−2i2i2i2i2i−2i−2i−2i−2i002i−2i00000022-2-20000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ31222-2-2-2-222i−2i2-22-22i−2i−2i−2i−2i−2i2i2i2i2i002i−2i000000-2-2220000000000000000000000002ζ6−2ζ62ζ2−2ζ200000000
χ32222-2-2-2-222i−2i2-22-22i−2i−2i−2i−2i−2i2i2i2i2i002i−2i000000-2-222000000000000000000000000−2ζ62ζ6−2ζ22ζ200000000
χ33222-2-2-2-22−2i2i2-22-2−2i2i2i2i2i2i−2i−2i−2i−2i00−2i2i000000-2-2220000000000000000000000002ζ2−2ζ22ζ6−2ζ600000000
χ34222-2-2-2-22−2i2i2-22-2−2i2i2i2i2i2i−2i−2i−2i−2i00−2i2i000000-2-222000000000000000000000000−2ζ22ζ2−2ζ62ζ600000000
χ35222-2-2-2-22−2i2i2-22-2−2i2i−2i−2i−2i−2i2i2i2i2i00−2i2i00000022-2-200000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ36222-2-2-2-22−2i2i2-22-2−2i2i−2i−2i−2i−2i2i2i2i2i00−2i2i00000022-2-20000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ3722-22-22-2-22i−2i0000−2i2ii2i2−i2−i2i2i2−i2−i22-2002i−2i00002−22−222−2−2i2i2−i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ3822-22-22-2-22i−2i0000−2i2ii2i2−i2−i2i2i2−i2−i22-2002i−2i00002−22−222−2−2i2i2−i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ3922-22-22-2-22i−2i0000−2i2ii2i2−i2−i2i2i2−i2−i2-2200−2i2i00002−22−2−2−222−i2−i2i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ4022-22-22-2-22i−2i0000−2i2ii2i2−i2−i2i2i2−i2−i2-2200−2i2i00002−22−2−2−222−i2−i2i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ4122-22-22-2-22i−2i0000−2i2i−i2−i2i2i2−i2−i2i2i22-2002i−2i0000−22−22−2−222−i2−i2i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ4222-22-22-2-22i−2i0000−2i2i−i2−i2i2i2−i2−i2i2i22-2002i−2i0000−22−22−2−222−i2−i2i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ4322-22-22-2-22i−2i0000−2i2i−i2−i2i2i2−i2−i2i2i2-2200−2i2i0000−22−2222−2−2i2i2−i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ4422-22-22-2-22i−2i0000−2i2i−i2−i2i2i2−i2−i2i2i2-2200−2i2i0000−22−2222−2−2i2i2−i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ4522-22-22-2-2−2i2i00002i−2ii2i2−i2−i2i2i2−i2−i22-200−2i2i0000−22−22−2−222i2i2−i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ4622-22-22-2-2−2i2i00002i−2ii2i2−i2−i2i2i2−i2−i22-200−2i2i0000−22−22−2−222i2i2−i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ4722-22-22-2-2−2i2i00002i−2ii2i2−i2−i2i2i2−i2−i2-22002i−2i0000−22−2222−2−2−i2−i2i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ4822-22-22-2-2−2i2i00002i−2ii2i2−i2−i2i2i2−i2−i2-22002i−2i0000−22−2222−2−2−i2−i2i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ4922-22-22-2-2−2i2i00002i−2i−i2−i2i2i2−i2−i2i2i22-200−2i2i00002−22−222−2−2−i2−i2i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ5022-22-22-2-2−2i2i00002i−2i−i2−i2i2i2−i2−i2i2i22-200−2i2i00002−22−222−2−2−i2−i2i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ5122-22-22-2-2−2i2i00002i−2i−i2−i2i2i2−i2−i2i2i2-22002i−2i00002−22−2−2−222i2i2−i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ5222-22-22-2-2−2i2i00002i−2i−i2−i2i2i2−i2−i2i2i2-22002i−2i00002−22−2−2−222i2i2−i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ53444-4-4-4-444i−4i-44-444i−4i0000000000−4i4i0000000000000000000000000000000000000000000000
χ54444-4-4-4-44−4i4i-44-44−4i4i00000000004i−4i0000000000000000000000000000000000000000000000
χ5544-4-44-44-4440000-4-42222−22−22−22−222222000000000022−22−2222000000000000000000000000000000000000
χ5644-4-44-44-4440000-4-4−22−2222222222−22−220000000000−222222−22000000000000000000000000000000000000
χ5744-4-44-44-4-4-40000442222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ5844-4-44-44-4-4-4000044−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000
χ594-444-4-44-40000000022−2222−2222−2222−22000000004i−4i000000002i2−2i22i2−2i20000000000000000000000000000
χ604-444-4-44-40000000022−2222−2222−2222−2200000000−4i4i00000000−2i22i2−2i22i20000000000000000000000000000
χ614-444-4-44-400000000−2222−2222−2222−2222000000004i−4i00000000−2i22i2−2i22i20000000000000000000000000000
χ624-444-4-44-400000000−2222−2222−2222−222200000000−4i4i000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-444-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000004i−4i00000022−2222−2200000000000000000000000000000000
χ644-44-444-4-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−4i4i000000−2222−222200000000000000000000000000000000
χ654-44-444-4-400000000−2i22i2−2i22i22i2−2i22i2−2i20000004i−4i000000−2222−222200000000000000000000000000000000
χ664-44-444-4-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000−4i4i00000022−2222−2200000000000000000000000000000000
χ674-4-444-4-440044-4-4004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-444-4-440044-4-400−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-444-4-4400-4-44400000000000000000000000000004-4-440000000000000000000000000000
χ704-4-444-4-4400-4-4440000000000000000000000000000-444-40000000000000000000000000000
χ714-4-4-4-4444004-4-44004-4-44-444-400000000000000000000000000000000000000000000000000
χ724-4-4-4-4444004-4-4400-444-44-4-4400000000000000000000000000000000000000000000000000
χ734-4-4-4-444400-444-40000000000000000000000004-4-4400000000000000000000000000000000
χ744-4-4-4-444400-444-4000000000000000000000000-444-400000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.