Finite Group Databasebeta

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C113×Dic11⋊C5 #38733244

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

Aliases

direct productC113×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C113)
unambiguous semidirect product(C11⋊C5)⋊(C4×C113)
unambiguous semidirect product(Dic11×C113)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C113
HallC11⋊C5×C113 ⋊ C4
HallDic11×C113 ⋊ C5
HallC11×C113 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C113
HallDic11 ⋊ C5×C113

Subgroups

subgroupG/H
center, hypercenterC2×C113AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C113
FrattiniC2AGL(1,𝔽11)×C113
Fitting, socleC2×C11×C113C2×C5
prime radicalC2×C11⋊C5×C113C2
cosocleC2×C11C2×C5×C113
LCSG ▷ C11
UCSC1 ◁ C2×C113

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4972

Conjugacy classes & character table

2486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24860, 11);