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C3×A5×C29⋊C7 #49141697

order36540
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC3×A5×C29⋊C7
unambiguous semidirect productC29⋊(C3×C7×A5)
unambiguous semidirect product(C3×C29)⋊(C7×A5)
unambiguous semidirect product(C29×A5)⋊(C3×C7)
unambiguous semidirect product(C3×C29×A5)⋊C7

Splittings

FittingC3×C29 ⋊ C7×A5
socle, HallC3×C29×A5 ⋊ C7
derivedC29×A5 ⋊ C3×C7
SylowC29 ⋊ C3×C7×A5

Subgroups

subgroupG/H
center, hypercenterC3A5×C29⋊C7
commutator, hypocenterC29×A5C3×C7
FrattiniC1G
FittingC3×C29C7×A5
socleC3×C29×A5C7
cosocleC29C3×C7×A5
LCSG ▷ C29×A5
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 435

A minimal faithful permutation representation — 2 generators on 37 points:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 539);