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C11×C3⋊#11759815 #45689593

order33462
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊#11759815
unambiguous semidirect productC3⋊(C11×#11759815)

Splittings

Fitting, socleC3×C11×C132 ⋊ C2×C3
derivedC3×C132 ⋊ C2×C3×C11
HallC3×C11×#92788 ⋊ C2
HallC11×C132 ⋊ C3×D3
HallC3×#92788 ⋊ C2×C11
SylowC132 ⋊ C3×D3×C11

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#11759815
commutator, cosocle, hypocenterC3×C132C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C132C2×C3
LCSG ▷ C3×C132
UCSC1 ◁ C11

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 5577

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

1023 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 101);