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C5×Dic3×C13×C17 #27210460

order13260
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C13×C17
unambiguous semidirect productC3⋊(C4×C5×C13×C17)

Splittings

derived, SylowC3 ⋊ C4×C5×C13×C17
HallC3×C5×C13×C17 ⋊ C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C13
HallC3×C5×C13 ⋊ C4×C17
HallC3×C17 ⋊ C4×C5×C13
HallC3×C13 ⋊ C4×C5×C17
HallC3×C5 ⋊ C4×C13×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13×C17D3
commutator, hypocenterC3C4×C5×C13×C17
FrattiniC2C5×D3×C13×C17
Fitting, socle, prime radicalC2×C3×C5×C13×C17C2
cosocleC2×C3C2×C5×C13×C17
LCSG ▷ C3
UCSC1 ◁ C2×C5×C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 13260

A minimal faithful permutation representation — 2 generators on 42 points:

(2,3)(4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,40,41,42);(1,2,3)

Conjugacy classes & character table

6630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 10);