Finite Group Databasebeta

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C4×C11⋊C5×#3861 #44568458

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11⋊C5×#3861
unambiguous semidirect product(C4×C11)⋊(C5×#3861)
unambiguous semidirect product(C4×C11×#3861)⋊C5

Splittings

Fitting, HallC4×C72×C11 ⋊ C3×C5
derived, HallC72×C11 ⋊ C3×C4×C5
HallC4×C72×C11⋊C5 ⋊ C3
HallC4×C11×#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC11×#3861 ⋊ C4×C5
HallC4×C72 ⋊ C3×C11⋊C5
SylowC72 ⋊ C3×C4×C11⋊C5
HallC4×C11 ⋊ C5×#3861
SylowC11 ⋊ C4×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC4C11⋊C5×#3861
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C2×C11⋊C5×#3861
FittingC4×C72×C11C3×C5
socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3861C2
LCSG ▷ C72×C11
UCSC1 ◁ C4

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 160);