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C5×C13×C3⋊#595 #27210553

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

Aliases

direct productC5×C13×C3⋊#595
unambiguous semidirect productC3⋊(C5×C13×#595)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC3×C17 ⋊ C4×C5×C13
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C13
HallC13×C17 ⋊ C5×Dic3
HallC3×C5×C13 ⋊ #595
HallC5×C17 ⋊ Dic3×C13
HallC3×C13 ⋊ C5×#595
SylowC17 ⋊ C5×Dic3×C13
HallC3×C5 ⋊ C13×#595
SylowC3 ⋊ C5×C13×#595

Subgroups

subgroupG/H
center, hypercenterC5×C13C3⋊#595
commutator, hypocenterC3×C17C4×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C5×C13×D17C2
cosocleC3×D17C2×C5×C13
LCSG ▷ C3×C17
UCSC1 ◁ 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:

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

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 103);