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C5×#13537 #11936257

order1280
nilpotency class4
isoclinismisoclinic class of #13304
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#13537

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5C2×D8
commutator, Frattini, cosocleC22×C8C23×C5
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5)(6,7,10,12)(8,13,9,11)(14,15)(16,18)(17,19)(20,21);(6,8,10,9)(7,11,12,13)(14,16,17,20)(15,18,19,21)(22,23)(24,27)(25,34)(26,30)(28,31)(29,32)(33,36)(35,37);(6,9,10,8)(7,11,12,13)(15,19)(18,21)(23,27)(24,31)(25,32)(28,29)(30,36)(33,37)(34,35)

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6525);