Finite Group Databasebeta

← Group #129558

Character table — Group #129558

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444224444444444888888888888161616161616161616161616161616162444888816161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-11-1-111-1ii−i−iii−i−i
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11-111-1-11−i−iii−i−iii
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii111-1-1-1-11ii−i−i−i−iii
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-1-11111-1−i−iiiii−i−i
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii1-11-1-111-1−i−iii−i−iii
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii-11-111-1-11ii−i−iii−i−i
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i111-1-1-1-11−i−iiiii−i−i
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i-1-1-11111-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
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χ222222-2-2-2-2222222-2-2-2-2-2-2000000000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-22-220000−i2−i2i2i2−i2−i2i2i20000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-2000000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22-22-20000−i2−i2i2i2−i2−i2i2i20000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-2000000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-22-220000i2i2−i2−i2i2i2−i2−i20000000000000000
χ252222-2-2-2-222-2-2-2-2-2-222220000000000002222−2−2−2−2−2−2−2−222222-2-22000022−2−2−2−2220000000000000000
χ262222-2-2-2-222-2-2-2-2-2-222220000000000002222−2−2−2−2−2−2−2−22222-222-20000−2−22222−2−20000000000000000
χ272222-2-2-2-222-2-2-2-2-2-22222000000000000−2−2−2−222222222−2−2−2−22-2-220000−2−22222−2−20000000000000000
χ282222-2-2-2-222-2-2-2-2-2-22222000000000000−2−2−2−222222222−2−2−2−2-222-2000022−2−2−2−2220000000000000000
χ292222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-222-2-200000000000000000000000000000000020002-2-200000000
χ302222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-222-2-2000000000000000000000000000000000-2000-22200000000
χ312222-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-2-2220000000000000000000000000000000020-22-200000000000
χ322222-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-2-22200000000000000000000000000000000-202-2200000000000
χ332222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2220000000000000000000000000000000020-2-2200000000000
χ342222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-22200000000000000000000000000000000-2022-200000000000
χ352222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2222222-2-20000000000000000000000000000000002000-22-200000000
χ362222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2222222-2-2000000000000000000000000000000000-20002-2200000000
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χ3822-2-222-2-22-22i−2i2i−2i2-22i−2i2i−2i0000000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2i2i-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ3922-2-222-2-22-22i−2i2i−2i2-22i−2i2i−2i000000000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002i−2i2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4022-2-222-2-22-22i−2i2i−2i2-22i−2i2i−2i000000000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2i2i-221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4122-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i0000000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002i−2i-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4222-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i0000000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000−2i2i2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4322-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i000000000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002i−2i-221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4422-2-222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i000000000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000−2i2i2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4522-2-222-2-2-222i−2i−2i2i-22−2i2i2i−2i2i2i−2i−2i2i2i−2i−2i2-22-200000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ4622-2-222-2-2-222i−2i−2i2i-22−2i2i2i−2i2i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ4722-2-222-2-2-222i−2i−2i2i-22−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i-22-22000000000000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6
χ4822-2-222-2-2-222i−2i−2i2i-22−2i2i2i−2i−2i−2i2i2i−2i−2i2i2i-22-2200000000000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ6
χ4922-2-222-2-2-22−2i2i2i−2i-222i−2i−2i2i2i2i−2i−2i2i2i−2i−2i-22-22000000000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2
χ5022-2-222-2-2-22−2i2i2i−2i-222i−2i−2i2i2i2i−2i−2i2i2i−2i−2i-22-2200000000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ2
χ5122-2-222-2-2-22−2i2i2i−2i-222i−2i−2i2i−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ5222-2-222-2-2-22−2i2i2i−2i-222i−2i−2i2i−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ5322-2-2-2-2222-22i−2i2i−2i-22−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-220000000000000000000000002ζ2−2ζ2−2ζ22ζ22ζ6−2ζ6−2ζ62ζ60000000000000000
χ5422-2-2-2-2222-22i−2i2i−2i-22−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22000000000000000000000000−2ζ22ζ22ζ2−2ζ2−2ζ62ζ62ζ6−2ζ60000000000000000
χ5522-2-2-2-2222-22i−2i2i−2i-22−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i-222-22ζ62ζ6−2ζ6−2ζ6−2ζ6−2ζ62ζ62ζ62ζ22ζ2−2ζ2−2ζ2−2ζ2−2ζ22ζ22ζ200000000000000000000000000000000
χ5622-2-2-2-2222-22i−2i2i−2i-22−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i-222-2−2ζ6−2ζ62ζ62ζ62ζ62ζ6−2ζ6−2ζ6−2ζ2−2ζ22ζ22ζ22ζ22ζ2−2ζ2−2ζ200000000000000000000000000000000
χ5722-2-2-2-2222-2−2i2i−2i2i-222i−2i2i−2i2i2i−2i−2i−2i−2i2i2i-222-22ζ22ζ2−2ζ2−2ζ2−2ζ2−2ζ22ζ22ζ22ζ62ζ6−2ζ6−2ζ6−2ζ6−2ζ62ζ62ζ600000000000000000000000000000000
χ5822-2-2-2-2222-2−2i2i−2i2i-222i−2i2i−2i2i2i−2i−2i−2i−2i2i2i-222-2−2ζ2−2ζ22ζ22ζ22ζ22ζ2−2ζ2−2ζ2−2ζ6−2ζ62ζ62ζ62ζ62ζ6−2ζ6−2ζ600000000000000000000000000000000
χ5922-2-2-2-2222-2−2i2i−2i2i-222i−2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-220000000000000000000000002ζ6−2ζ6−2ζ62ζ62ζ2−2ζ2−2ζ22ζ20000000000000000
χ6022-2-2-2-2222-2−2i2i−2i2i-222i−2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22000000000000000000000000−2ζ62ζ62ζ6−2ζ6−2ζ22ζ22ζ2−2ζ20000000000000000
χ6144444444-4-444-4-4-4-4-4-444000000000000000000000000000000000000000000000000000000000000
χ6244444444-4-4-4-444-4-444-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-444i−4i−4i4i4-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-44−4i4i4i−4i4-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−2200002ζ−2ζ2ζ−2ζ2ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ32ζ7−2ζ72ζ7−2ζ700000000000000000000000000000000
χ664-44-44i−4i4i−4i0000000000002i2−2i22i2−2i222−2222−220000−2ζ2ζ−2ζ2ζ−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ3−2ζ72ζ7−2ζ72ζ700000000000000000000000000000000
χ674-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−222200002ζ5−2ζ52ζ5−2ζ5−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ72ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000
χ684-44-44i−4i4i−4i000000000000−2i22i2−2i22i2−2222−22220000−2ζ52ζ5−2ζ52ζ52ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ7−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000
χ694-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−222200002ζ3−2ζ32ζ3−2ζ3−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ2ζ5−2ζ52ζ5−2ζ500000000000000000000000000000000
χ704-44-4−4i4i−4i4i0000000000002i2−2i22i2−2i2−2222−22220000−2ζ32ζ3−2ζ32ζ32ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ−2ζ52ζ5−2ζ52ζ500000000000000000000000000000000
χ714-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−2200002ζ7−2ζ72ζ7−2ζ72ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ52ζ−2ζ2ζ−2ζ00000000000000000000000000000000
χ724-44-4−4i4i−4i4i000000000000−2i22i2−2i22i222−2222−220000−2ζ72ζ7−2ζ72ζ7−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ5−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ734-4-444i−4i−4i4i00000000000022−22−2222−2i22i22i2−2i200002ζ−2ζ−2ζ2ζ2ζ5−2ζ5−2ζ52ζ52ζ3−2ζ3−2ζ32ζ32ζ7−2ζ7−2ζ72ζ700000000000000000000000000000000
χ744-4-444i−4i−4i4i00000000000022−22−2222−2i22i22i2−2i20000−2ζ2ζ2ζ−2ζ−2ζ52ζ52ζ5−2ζ5−2ζ32ζ32ζ3−2ζ3−2ζ72ζ72ζ7−2ζ700000000000000000000000000000000
χ754-4-444i−4i−4i4i000000000000−222222−222i2−2i2−2i22i200002ζ5−2ζ5−2ζ52ζ5−2ζ2ζ2ζ−2ζ−2ζ72ζ72ζ7−2ζ72ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ764-4-444i−4i−4i4i000000000000−222222−222i2−2i2−2i22i20000−2ζ52ζ52ζ5−2ζ52ζ−2ζ−2ζ2ζ2ζ7−2ζ7−2ζ72ζ7−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ774-4-44−4i4i4i−4i00000000000022−22−22222i2−2i2−2i22i200002ζ7−2ζ7−2ζ72ζ72ζ3−2ζ3−2ζ32ζ32ζ5−2ζ5−2ζ52ζ52ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ784-4-44−4i4i4i−4i00000000000022−22−22222i2−2i2−2i22i20000−2ζ72ζ72ζ7−2ζ7−2ζ32ζ32ζ3−2ζ3−2ζ52ζ52ζ5−2ζ5−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ794-4-44−4i4i4i−4i000000000000−222222−22−2i22i22i2−2i200002ζ3−2ζ3−2ζ32ζ3−2ζ72ζ72ζ7−2ζ7−2ζ2ζ2ζ−2ζ2ζ5−2ζ5−2ζ52ζ500000000000000000000000000000000
χ804-4-44−4i4i4i−4i000000000000−222222−22−2i22i22i2−2i20000−2ζ32ζ32ζ3−2ζ32ζ7−2ζ7−2ζ72ζ72ζ−2ζ−2ζ2ζ−2ζ52ζ52ζ5−2ζ500000000000000000000000000000000

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