Finite Group Databasebeta

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C131×Dic11⋊C5 #43273668

order28820
automorphism?
homologyAbelianization (H1) = C4×C5×C131 · Schur multiplier (H2) = C1

Aliases

direct productC131×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C131)
unambiguous semidirect product(C11⋊C5)⋊(C4×C131)

Splittings

derived, SylowC11 ⋊ C4×C5×C131
HallC11⋊C5×C131 ⋊ C4
HallDic11×C131 ⋊ C5
HallC11×C131 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C131
HallDic11 ⋊ C5×C131

Subgroups

subgroupG/H
center, hypercenterC2×C131AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C131
FrattiniC2AGL(1,𝔽11)×C131
Fitting, socleC2×C11×C131C2×C5
prime radicalC2×C11⋊C5×C131C2
cosocleC2×C11C2×C5×C131
LCSG ▷ C11
UCSC1 ◁ C2×C131

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5764

Conjugacy classes & character table

2882 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28820, 22);