Finite Group Databasebeta

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C107×Dic11⋊C5 #37555322

order23540
automorphism?
homologyAbelianization (H1) = C4×C5×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C107)
unambiguous semidirect product(C11⋊C5)⋊(C4×C107)
unambiguous semidirect product(Dic11×C107)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C107
HallC11⋊C5×C107 ⋊ C4
HallDic11×C107 ⋊ C5
HallC11×C107 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C107
HallDic11 ⋊ C5×C107

Subgroups

subgroupG/H
center, hypercenterC2×C107AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C107
FrattiniC2C107×AGL(1,𝔽11)
Fitting, socleC2×C11×C107C2×C5
prime radicalC2×C11⋊C5×C107C2
cosocleC2×C11C2×C5×C107
LCSG ▷ C11
UCSC1 ◁ C2×C107

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4708

Conjugacy classes & character table

2354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23540, 11);