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C5×C3⋊(#131⋊C3) #13086232

order1440
isoclinismisoclinic class of C3⋊(#41⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(#131⋊C3)
unambiguous semidirect productC3⋊(C5×#131⋊C3)
unambiguous semidirect product#948⋊(C3×C5)
unambiguous semidirect product(C5×#948)⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5D3×A4
commutator, hypocenterC3×Q8C3×C4×C5
FrattiniC4C5×D3×A4
FittingC3×C5×#41C2×C3
socleC2×C3×C5C4×A4
prime radicalC3×C5×#41⋊C3C2
cosocleC3×#41C2×C3×C5
LCSG ▷ C3×Q8
UCSC1 ◁ C4×C5

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8,12,11,15,18,25)(9,26,17,23,21,29,31,36,10,13,30,24,20,28,33,35,19,14,16,34,22,27,32,37)(39,40);(6,21,11,19)(7,28,15,26)(8,32,18,30)(9,10,20,22)(12,36,25,34)(13,14,27,29)(16,17,31,33)(23,24,35,37)(38,39,40)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2549);