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C5×#2070⋊C3 #14510697

order1920
isoclinismisoclinic class of #2069⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#2070⋊C3
unambiguous semidirect product#2070⋊(C3×C5)
unambiguous semidirect product(C5×#2070)⋊C3

Splittings

Fitting, HallC5×#2070 ⋊ C3
Sylow#2070 ⋊ C3×C5

Subgroups

subgroupG/H
center, socleC2×C5#396⋊C3
commutator, cosocle, hypocenter#338C2×C3×C5
FrattiniC22×C4C2×C5×A4
FittingC5×#2070C3
prime radicalC5×#338⋊C3C2
hypercenterC4×C5#126⋊C3
LCSG ▷ #338
UCSC1 ◁ C2×C5 ◁ C4×C5

112 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)(6,7,11,15)(8,28,9,12,17,13,19,29,23,31,16,20)(10,24,27,14)(18,37,22,34,36,35,25,32,26,30,21,33);(6,21,10,16,11,36,27,17)(7,32,14,28,15,37,24,29)(8,23,18,26,19,9,25,22)(12,20,30,35,31,13,34,33)

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236395);