Finite Group Databasebeta

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C3×C5×C11×C41⋊C5 #46799092

order33825
automorphism?
homologyAbelianization (H1) = C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C11×C41⋊C5
unambiguous semidirect productC41⋊(C3×C52×C11)
unambiguous semidirect product(C3×C41)⋊(C52×C11)
unambiguous semidirect product(C5×C41)⋊(C3×C5×C11)
unambiguous semidirect product(C3×C5×C41)⋊(C5×C11)

Splittings

Fitting, socleC3×C5×C11×C41 ⋊ C5
derived, SylowC41 ⋊ C3×C52×C11
HallC3×C11×C41 ⋊ C52
HallC11×C41 ⋊ C3×C52
HallC3×C41 ⋊ C52×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11C41⋊C5
commutator, cosocle, hypocenterC41C3×C52×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C41C5
LCSG ▷ C41
UCSC1 ◁ C3×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6765

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33825, 10);