Finite Group Databasebeta

← Group #72267662

Character table — Group #72267662

Order 5120.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size115555551616202020202020202020202020202020204040404040404040404040408080256256256256256256256256256256256256256256256256
order12222222444444444444444444444444444444445555101010102020202020202020
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−ζ2−ζ14−ζ6−ζ18−ζ2−ζ14−ζ6−ζ18−ζ2−ζ2−ζ14−ζ14−ζ6−ζ6−ζ18−ζ18
χ31111111111111111111111111111111111111111−ζ14−ζ18−ζ2−ζ6−ζ14−ζ18−ζ2−ζ6−ζ14−ζ14−ζ18−ζ18−ζ2−ζ2−ζ6−ζ6
χ41111111111111111111111111111111111111111−ζ6−ζ2−ζ18−ζ14−ζ6−ζ2−ζ18−ζ14−ζ6−ζ6−ζ2−ζ2−ζ18−ζ18−ζ14−ζ14
χ51111111111111111111111111111111111111111−ζ18−ζ6−ζ14−ζ2−ζ18−ζ6−ζ14−ζ2−ζ18−ζ18−ζ6−ζ6−ζ14−ζ14−ζ2−ζ2
χ611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1-1-1
χ711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−ζ2−ζ14−ζ6−ζ18−ζ2−ζ14−ζ6−ζ18ζ2ζ2ζ14ζ14ζ6ζ6ζ18ζ18
χ811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−ζ14−ζ18−ζ2−ζ6−ζ14−ζ18−ζ2−ζ6ζ14ζ14ζ18ζ18ζ2ζ2ζ6ζ6
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−ζ6−ζ2−ζ18−ζ14−ζ6−ζ2−ζ18−ζ14ζ6ζ6ζ2ζ2ζ18ζ18ζ14ζ14
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−ζ18−ζ6−ζ14−ζ2−ζ18−ζ6−ζ14−ζ2ζ18ζ18ζ6ζ6ζ14ζ14ζ2ζ2
χ111-111-1-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1i−i1111-1-1-1-1i−ii−ii−ii−i
χ121-111-1-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1i−i−ζ2−ζ14−ζ6−ζ18ζ2ζ14ζ6ζ18−ζ7ζ7−ζ19ζ19−ζ11ζ11−ζ3ζ3
χ131-111-1-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1i−i−ζ14−ζ18−ζ2−ζ6ζ14ζ18ζ2ζ6−ζ19ζ19−ζ3ζ3−ζ7ζ7−ζ11ζ11
χ141-111-1-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1i−i−ζ6−ζ2−ζ18−ζ14ζ6ζ2ζ18ζ14−ζ11ζ11−ζ7ζ7−ζ3ζ3−ζ19ζ19
χ151-111-1-1-11i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1i−i−ζ18−ζ6−ζ14−ζ2ζ18ζ6ζ14ζ2−ζ3ζ3−ζ11ζ11−ζ19ζ19−ζ7ζ7
χ161-111-1-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−ii1111-1-1-1-1−ii−ii−ii−ii
χ171-111-1-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−ii−ζ2−ζ14−ζ6−ζ18ζ2ζ14ζ6ζ18ζ7−ζ7ζ19−ζ19ζ11−ζ11ζ3−ζ3
χ181-111-1-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−ii−ζ14−ζ18−ζ2−ζ6ζ14ζ18ζ2ζ6ζ19−ζ19ζ3−ζ3ζ7−ζ7ζ11−ζ11
χ191-111-1-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−ii−ζ6−ζ2−ζ18−ζ14ζ6ζ2ζ18ζ14ζ11−ζ11ζ7−ζ7ζ3−ζ3ζ19−ζ19
χ201-111-1-1-11−ii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−ii−ζ18−ζ6−ζ14−ζ2ζ18ζ6ζ14ζ2ζ3−ζ3ζ11−ζ11ζ19−ζ19ζ7−ζ7
χ21555555555511111111111111111111-3-31111-3-3-3-30000000000000000
χ2255555555551111-3-3-3-31111-3-3-3-311-3-31111-3-311110000000000000000
χ235555555555-3-3-3-31111-3-3-3-31111-3-31111-3-31111110000000000000000
χ2455555555-5-53333-1-1-1-13333-1-1-1-1-3-31111-3-31111-1-10000000000000000
χ2555555555-5-5-1-1-1-13333-1-1-1-1333311-3-31111-3-311-1-10000000000000000
χ2655555555-5-5-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-3-31111-3-3330000000000000000
χ275-555-5-5-555i−5iiiiiiiii−i−i−i−i−i−i−i−i1111-3-3-1-1-1-133−3i3i0000000000000000
χ285-555-5-5-555i−5iiiii−3i−3i−3i−3i−i−i−i−i3i3i3i3i11-3-311-1-133-1-1i−i0000000000000000
χ295-555-5-5-555i−5i−3i−3i−3i−3iiiii3i3i3i3i−i−i−i−i-3-3111133-1-1-1-1i−i0000000000000000
χ305-555-5-5-55−5i5i3i3i3i3i−i−i−i−i−3i−3i−3i−3iiiii-3-3111133-1-1-1-1−ii0000000000000000
χ315-555-5-5-55−5i5i−i−i−i−i3i3i3i3iiiii−3i−3i−3i−3i11-3-311-1-133-1-1−ii0000000000000000
χ325-555-5-5-55−5i5i−i−i−i−i−i−i−i−iiiiiiiii1111-3-3-1-1-1-1333i−3i0000000000000000
χ33101022-622-600004i−4i004i−4i004i−4i004i−4i2-22-22-22-22-22-2000000000000000000
χ34101022-622-600004i−4i00−4i4i004i−4i00−4i4i-22-222-2-22-222-2000000000000000000
χ35101022-622-60000−4i4i004i−4i00−4i4i004i−4i-22-222-2-22-222-2000000000000000000
χ36101022-622-60000−4i4i00−4i4i00−4i4i00−4i4i2-22-22-22-22-22-2000000000000000000
χ37101022-622-6004i−4i004i−4i004i−4i004i−4i002-2-22-222-2-22-22000000000000000000
χ38101022-622-6004i−4i00−4i4i004i−4i00−4i4i00-222-2-22-222-2-22000000000000000000
χ39101022-622-600−4i4i004i−4i00−4i4i004i−4i00-222-2-22-222-2-22000000000000000000
χ40101022-622-600−4i4i00−4i4i00−4i4i00−4i4i002-2-22-222-2-22-22000000000000000000
χ4110-10226-2-2-600004-4004-400-4400-442-22-22-2-22-22-22000000000000000000
χ4210-10226-2-2-600004-400-4400-44004-4-22-222-22-22-2-22000000000000000000
χ4310-10226-2-2-60000-44004-4004-400-44-22-222-22-22-2-22000000000000000000
χ4410-10226-2-2-60000-4400-44004-4004-42-22-22-2-22-22-22000000000000000000
χ4510-10226-2-2-6004-4004-400-4400-44002-2-22-22-222-22-2000000000000000000
χ4610-10226-2-2-6004-400-4400-44004-400-222-2-222-2-222-2000000000000000000
χ4710-10226-2-2-600-44004-4004-400-4400-222-2-222-2-222-2000000000000000000
χ4810-10226-2-2-600-4400-44004-4004-4002-2-22-22-222-22-2000000000000000000
χ4920204-1244-12400000044-4-4000044-4-4000000000000000000000000000000
χ5020204-1244-124000000-4-4440000-4-444000000000000000000000000000000
χ512020-1244-12440044-4-4000044-4-40000000000000000000000000000000000
χ522020-1244-124400-4-4440000-4-4440000000000000000000000000000000000
χ5320-204-12-4-41240000004i4i−4i−4i0000−4i−4i4i4i000000000000000000000000000000
χ5420-204-12-4-4124000000−4i−4i4i4i00004i4i−4i−4i000000000000000000000000000000
χ5520-20-124-412-44004i4i−4i−4i0000−4i−4i4i4i0000000000000000000000000000000000
χ5620-20-124-412-4400−4i−4i4i4i00004i4i−4i−4i0000000000000000000000000000000000

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