Finite Group Databasebeta

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C4×C11⋊C5×C113 #38733235

order24860
automorphism?
homologyAbelianization (H1) = C4×C5×C113 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11⋊C5×C113
unambiguous semidirect product(C4×C11)⋊(C5×C113)
unambiguous semidirect product(C4×C11×C113)⋊C5

Splittings

Fitting, HallC4×C11×C113 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C113
HallC11×C113 ⋊ C4×C5
HallC4×C11 ⋊ C5×C113

Subgroups

subgroupG/H
center, hypercenterC4×C113C11⋊C5
commutator, hypocenterC11C4×C5×C113
FrattiniC2C2×C11⋊C5×C113
FittingC4×C11×C113C5
socleC2×C11×C113C2×C5
prime radicalC2×C11⋊C5×C113C2
cosocleC2×C11C2×C5×C113
LCSG ▷ C11
UCSC1 ◁ C4×C113

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4972

Conjugacy classes & character table

3164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24860, 2);