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C13×C3⋊#66775 #27210566

order13260
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊#66775
unambiguous semidirect productC3⋊(C13×#66775)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC3×C5×C17 ⋊ C4×C13
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ AGL(1,𝔽5)
HallC13×C17 ⋊ ΓL(1,𝔽16)
HallC3×C5×C13 ⋊ #595
HallC5×C17 ⋊ Dic3×C13
HallC5×C13 ⋊ C3⋊#595
HallC3×C17 ⋊ C13×AGL(1,𝔽5)
HallC3×C13 ⋊ #66775
SylowC17 ⋊ C13×ΓL(1,𝔽16)
HallC3×C5 ⋊ C13×#595
SylowC5 ⋊ C13×C3⋊#595
SylowC3 ⋊ C13×#66775

Subgroups

subgroupG/H
center, hypercenterC13C3⋊#66775
commutator, hypocenterC3×C5×C17C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C13×D85C2
cosocleC3×D85C2×C13
LCSG ▷ C3×C5×C17
UCSC1 ◁ 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:

(2,3,4,6)(5,8,9,13)(7,12,10,11)(14,16,17,15)(19,20,21,22)(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)(18,19,20,22,21)(23,24,25)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 116);