Finite Group Databasebeta

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C3×C132×C11⋊C5 #42124200

order27885
automorphism?
homologyAbelianization (H1) = C3×C5×C132 · Schur multiplier (H2) = C13

Aliases

direct productC3×C132×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C132)
unambiguous semidirect product(C3×C11)⋊(C5×C132)
unambiguous semidirect product(C3×C11×C13)⋊(C5×C13)
unambiguous semidirect product(C3×C11×C132)⋊C5

Splittings

Fitting, socle, HallC3×C11×C132 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C132
HallC11×C132 ⋊ C3×C5
HallC3×C11 ⋊ C5×C132

Subgroups

subgroupG/H
center, hypercenterC3×C132C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C132
FrattiniC1G
Fitting, socleC3×C11×C132C5
LCSG ▷ C11
UCSC1 ◁ C3×C132

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5577

Conjugacy classes & character table

3549 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27885, 9);