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C3×C11⋊((C13⋊C3)⋊D13) #45689579

order33462
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊((C13⋊C3)⋊D13)
unambiguous semidirect productC11⋊(C3×(C13⋊C3)⋊D13)
unambiguous semidirect product(C13⋊C3)⋊(C3×D143)

Splittings

Fitting, socleC3×C11×C132 ⋊ C2×C3
derived, HallC11×C132 ⋊ C2×C32
HallC3×C11×C13×C13⋊C3 ⋊ C2
HallC11⋊(C13⋊D13) ⋊ C32
HallC3×C13×C13⋊C3 ⋊ D11
SylowC132 ⋊ C32×D11
SylowC11 ⋊ C3×(C13⋊C3)⋊D13

Subgroups

subgroupG/H
center, hypercenterC3C11⋊((C13⋊C3)⋊D13)
commutator, cosocle, hypocenterC11×C132C2×C32
FrattiniC1G
Fitting, socleC3×C11×C132C2×C3
LCSG ▷ C11×C132
UCSC1 ◁ C3

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 1287

A minimal faithful permutation representation — 2 generators on 40 points:

(5,6)(7,8)(9,10)(11,12)(13,14)(16,20,21,17,18,22)(19,26,25,23,24,27)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40);(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(15,16,19,18,22,25,24,26,27,21,20,23,17)(28,29,31,33,35,37,39,40,38,36,34,32,30)

Conjugacy classes & character table

1515 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 87);