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C5×#1747⋊C3 #14510682

order1920
isoclinismisoclinic class of #338⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#1747⋊C3
unambiguous semidirect product#1747⋊(C3×C5)
unambiguous semidirect product(C5×#1747)⋊C3

Splittings

Fitting, HallC5×#1747 ⋊ C3
Sylow#1747 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC5×C8C42⋊C3
commutator, cosocle, hypocenter#338C2×C3×C5
FrattiniC22×C4C2×C5×A4
FittingC5×#1747C3
socleC2×C5#376⋊C3
prime radicalC5×#338⋊C3C2
LCSG ▷ #338
UCSC1 ◁ C5×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 160

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236380);