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C4×C5×C17×C13⋊C3 #27210452

order13260
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C17×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C3×C5×C17)
unambiguous semidirect product(C4×C5×C13)⋊(C3×C17)
unambiguous semidirect product(C4×C13×C17)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C13×C17)⋊C3

Splittings

Fitting, HallC4×C5×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C5×C17
HallC5×C13×C17 ⋊ C3×C4
HallC4×C13×C17 ⋊ C3×C5
HallC4×C5×C13 ⋊ C3×C17
HallC13×C17 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C17
HallC4×C13 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C5×C17C13⋊C3
commutator, hypocenterC13C3×C4×C5×C17
FrattiniC2C2×C5×C17×C13⋊C3
FittingC4×C5×C13×C17C3
socleC2×C5×C13×C17C2×C3
prime radicalC2×C5×C17×C13⋊C3C2
cosocleC2×C13C2×C3×C5×C17
LCSG ▷ C13
UCSC1 ◁ C4×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 4420

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 2);