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C43×C9⋊#261 #34117451

order20124
isoclinismisoclinic class of C9⋊#261
automorphism?
homologyAbelianization (H1) = C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×C9⋊#261
unambiguous semidirect productC9⋊(C43×#261)

Splittings

Fitting, HallC9×C13×C43 ⋊ C4
derived, HallC9×C13 ⋊ C4×C43
HallC13×C43 ⋊ Dic9
HallC9×C43 ⋊ #261
SylowC13 ⋊ Dic9×C43
SylowC9 ⋊ C43×#261

Subgroups

subgroupG/H
center, hypercenterC43C9⋊#261
commutator, hypocenterC9×C13C4×C43
FrattiniC3C43×C3⋊#261
FittingC9×C13×C43C4
socleC3×C13×C43Dic3
prime radicalC3×D13×C43D3
cosocleC9×D13C2×C43
LCSG ▷ C9×C13
UCSC1 ◁ C43

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 5031

A minimal faithful permutation representation — 2 generators on 65 points:

(2,6,4,3)(5,10,9,8)(7,11,13,12)(15,17)(16,20)(18,19)(21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(1,2,5,10,12,3,7,13,6,11,8,9,4)(14,22,17,20,19,18,16,15,21)

Conjugacy classes & character table

1677 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 54);