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C3×C5×C23⋊C11 #16838282

order3795
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C23⋊C11
unambiguous semidirect productC23⋊(C3×C5×C11)
unambiguous semidirect product(C3×C23)⋊(C5×C11)
unambiguous semidirect product(C5×C23)⋊(C3×C11)
unambiguous semidirect product(C3×C5×C23)⋊C11

Splittings

Fitting, socle, HallC3×C5×C23 ⋊ C11
derived, SylowC23 ⋊ C3×C5×C11
HallC5×C23 ⋊ C3×C11
HallC3×C23 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5C23⋊C11
commutator, cosocle, hypocenterC23C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C23C11
LCSG ▷ C23
UCSC1 ◁ C3×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 345

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9×C23⋊C11, C32×C5×C23⋊C11, C5×A4×C23⋊C11, …
maximal normal subgroup ofC5×C9×C23⋊C11, C32×C5×C23⋊C11, C3×C25×C23⋊C11, …
maximal quotient ofC5×C9×C23⋊C11, C32×C5×C23⋊C11, C5×A4×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3795, 2);