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C17×C3⋊#63118 #27210583

order13260
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊#63118
unambiguous semidirect productC3⋊(C17×#63118)

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C17
HallC5×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ #261
HallC13×C17 ⋊ Dic15
HallC5×C17 ⋊ C3⋊#261
HallC5×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ #63118
HallC3×C13 ⋊ C17×Dic5
HallC3×C5 ⋊ C17×#261
SylowC13 ⋊ C17×Dic15
SylowC5 ⋊ C17×C3⋊#261
SylowC3 ⋊ C17×#63118

Subgroups

subgroupG/H
center, hypercenterC17C3⋊#63118
commutator, hypocenterC3×C5×C13C4×C17
FrattiniC1G
Fitting, socleC3×C5×C13×C17C4
prime radicalC3×C5×C17×D13C2
cosocleC3×C5×D13C2×C17
LCSG ▷ C3×C5×C13
UCSC1 ◁ C17

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

Conjugacy classes & character table

1071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 133);