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C3×C5×C13×#595 #27210518

order13260
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×#595

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, SylowC17 ⋊ C3×C4×C5×C13
HallC5×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C13
HallC13×C17 ⋊ C3×C4×C5
HallC5×C17 ⋊ C3×C4×C13
HallC3×C17 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13#595
commutator, hypocenterC17C3×C4×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C5×C13×D17C2
cosocleD17C2×C3×C5×C13
LCSG ▷ C17
UCSC1 ◁ C3×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 68);