Finite Group Databasebeta

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C72×C3⋊(Dic11⋊C5) #44568465

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C72×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C72×Dic3)
unambiguous semidirect productDic33⋊(C5×C72)
unambiguous semidirect product(C7×Dic33)⋊(C5×C7)
unambiguous semidirect product(C72×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C72
HallC3×C72×C11⋊C5 ⋊ C4
HallC72×Dic33 ⋊ C5
HallC72×C11⋊C5 ⋊ Dic3
HallC3×C72×C11 ⋊ C4×C5
HallC72×C11 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C4×C72
HallC3×C72 ⋊ Dic11⋊C5
HallDic33 ⋊ C5×C72
HallC11⋊C5 ⋊ C72×Dic3
SylowC11 ⋊ C5×C72×Dic3
SylowC3 ⋊ C72×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C72C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C5×C72
FrattiniC2C72×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C3×C11C2×C5×C72
LCSG ▷ C3×C11
UCSC1 ◁ C2×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 167);