Finite Group Databasebeta

← Group #72267832

Character table — Group #72267832

Order 5120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111555555555555404040404040404040404040404040404040404040404040256256256256256256256256256256256256256256256256
order12222222222222224444444444444444444444445555101010101010101010101010
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−ζ2−ζ14−ζ6−ζ18−ζ2−ζ2−ζ2−ζ14−ζ14−ζ14−ζ6−ζ6−ζ6−ζ18−ζ18−ζ18
χ31111111111111111111111111111111111111111−ζ14−ζ18−ζ2−ζ6−ζ14−ζ14−ζ14−ζ18−ζ18−ζ18−ζ2−ζ2−ζ2−ζ6−ζ6−ζ6
χ41111111111111111111111111111111111111111−ζ6−ζ2−ζ18−ζ14−ζ6−ζ6−ζ6−ζ2−ζ2−ζ2−ζ18−ζ18−ζ18−ζ14−ζ14−ζ14
χ51111111111111111111111111111111111111111−ζ18−ζ6−ζ14−ζ2−ζ18−ζ18−ζ18−ζ6−ζ6−ζ6−ζ14−ζ14−ζ14−ζ2−ζ2−ζ2
χ644-4-444444-4-4-4-4-44-4000000000000000000000000-1-1-1-111-111-111-111-1
χ744-4-444444-4-4-4-4-44-4000000000000000000000000ζ2ζ14ζ6ζ18−ζ2−ζ2ζ2−ζ14−ζ14ζ14−ζ6−ζ6ζ6−ζ18−ζ18ζ18
χ844-4-444444-4-4-4-4-44-4000000000000000000000000ζ14ζ18ζ2ζ6−ζ14−ζ14ζ14−ζ18−ζ18ζ18−ζ2−ζ2ζ2−ζ6−ζ6ζ6
χ944-4-444444-4-4-4-4-44-4000000000000000000000000ζ6ζ2ζ18ζ14−ζ6−ζ6ζ6−ζ2−ζ2ζ2−ζ18−ζ18ζ18−ζ14−ζ14ζ14
χ1044-4-444444-4-4-4-4-44-4000000000000000000000000ζ18ζ6ζ14ζ2−ζ18−ζ18ζ18−ζ6−ζ6ζ6−ζ14−ζ14ζ14−ζ2−ζ2ζ2
χ114-44-4444-4-444-4-4-4-44000000000000000000000000-1-1-1-11-111-111-111-11
χ124-44-4444-4-444-4-4-4-44000000000000000000000000ζ2ζ14ζ6ζ18−ζ2ζ2−ζ2−ζ14ζ14−ζ14−ζ6ζ6−ζ6−ζ18ζ18−ζ18
χ134-44-4444-4-444-4-4-4-44000000000000000000000000ζ14ζ18ζ2ζ6−ζ14ζ14−ζ14−ζ18ζ18−ζ18−ζ2ζ2−ζ2−ζ6ζ6−ζ6
χ144-44-4444-4-444-4-4-4-44000000000000000000000000ζ6ζ2ζ18ζ14−ζ6ζ6−ζ6−ζ2ζ2−ζ2−ζ18ζ18−ζ18−ζ14ζ14−ζ14
χ154-44-4444-4-444-4-4-4-44000000000000000000000000ζ18ζ6ζ14ζ2−ζ18ζ18−ζ18−ζ6ζ6−ζ6−ζ14ζ14−ζ14−ζ2ζ2−ζ2
χ164-4-44444-4-4-4-4444-4-4000000000000000000000000-1-1-1-1-111-111-111-111
χ174-4-44444-4-4-4-4444-4-4000000000000000000000000ζ2ζ14ζ6ζ18ζ2−ζ2−ζ2ζ14−ζ14−ζ14ζ6−ζ6−ζ6ζ18−ζ18−ζ18
χ184-4-44444-4-4-4-4444-4-4000000000000000000000000ζ14ζ18ζ2ζ6ζ14−ζ14−ζ14ζ18−ζ18−ζ18ζ2−ζ2−ζ2ζ6−ζ6−ζ6
χ194-4-44444-4-4-4-4444-4-4000000000000000000000000ζ6ζ2ζ18ζ14ζ6−ζ6−ζ6ζ2−ζ2−ζ2ζ18−ζ18−ζ18ζ14−ζ14−ζ14
χ204-4-44444-4-4-4-4444-4-4000000000000000000000000ζ18ζ6ζ14ζ2ζ18−ζ18−ζ18ζ6−ζ6−ζ6ζ14−ζ14−ζ14ζ2−ζ2−ζ2
χ2155555555555555551111111111111111-3-3-3-3-3-3-3-30000000000000000
χ22555555555555555511111111-3-3-3-3-3-3-3-3111111110000000000000000
χ235555555555555555-3-3-3-3-3-3-3-311111111111111110000000000000000
χ241010101022-62-62-622-6222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000
χ251010101022-62-62-622-6222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000
χ261010101022-62-62-622-622-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000
χ271010101022-62-62-622-622-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000
χ281010-10-102-62226-26-2-2-6-20000000022-2-222-2-2000044-4-40000000000000000
χ291010-10-102-62226-26-2-2-6-20000000022-2-222-2-20000-4-4440000000000000000
χ301010-10-102-62226-26-2-2-6-200000000-2-222-2-22244-4-400000000000000000000
χ311010-10-102-62226-26-2-2-6-200000000-2-222-2-222-4-44400000000000000000000
χ321010-10-10-622-62-2-2-26-22600004i4i−4i−4i22-2-2-2-222000000000000000000000000
χ331010-10-10-622-62-2-2-26-2260000−4i−4i4i4i22-2-2-2-222000000000000000000000000
χ341010-10-10-622-62-2-2-26-2264i4i−4i−4i0000-2-22222-2-2000000000000000000000000
χ351010-10-10-622-62-2-2-26-226−4i−4i4i4i0000-2-22222-2-2000000000000000000000000
χ3610-1010-102-62-2-2-626-2-26200004i−4i4i−4i000000002-22-22-22-20000000000000000
χ3710-1010-102-62-2-2-626-2-2620000−4i4i−4i4i000000002-22-22-22-20000000000000000
χ3810-1010-102-62-2-2-626-2-2624i−4i4i−4i000000000000-22-22-22-220000000000000000
χ3910-1010-102-62-2-2-626-2-262−4i4i−4i4i000000000000-22-22-22-220000000000000000
χ4010-1010-10-6226-222-26-2-2-60000000000004-44-42-22-2-22-220000000000000000
χ4110-1010-10-6226-222-26-2-2-6000000000000-44-442-22-2-22-220000000000000000
χ4210-1010-10-6226-222-26-2-2-6000000004-44-40000-22-222-22-20000000000000000
χ4310-1010-10-6226-222-26-2-2-600000000-44-440000-22-222-22-20000000000000000
χ4410-10-10102-62-2-26-2-6226-22-2-222-2-2200004-4-44000000000000000000000000
χ4510-10-10102-62-2-26-2-6226-22-2-222-2-220000-444-4000000000000000000000000
χ4610-10-10102-62-2-26-2-6226-2-222-2-222-24-4-440000000000000000000000000000
χ4710-10-10102-62-2-26-2-6226-2-222-2-222-2-444-40000000000000000000000000000
χ4810-10-1010-6226-2-2-22-62-262-2-22-222-2000000004-4-4400000000000000000000
χ4910-10-1010-6226-2-2-22-62-262-2-22-222-200000000-444-400000000000000000000
χ5010-10-1010-6226-2-2-22-62-26-222-22-2-220000000000004-4-440000000000000000
χ5110-10-1010-6226-2-2-22-62-26-222-22-2-22000000000000-444-40000000000000000
χ52202020204-12444-124-1244-1240000000000000000000000000000000000000000
χ5320202020-1244-124444-1244-120000000000000000000000000000000000000000
χ542020-20-2044-124-12-412-4-4124-40000000000000000000000000000000000000000
χ5520-2020-2044-12-4124-12-4-412-440000000000000000000000000000000000000000
χ5620-20-202044-12-412-41244-12-4-40000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.