Finite Group Databasebeta

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C72×A4×C11⋊C5 #44568611

order32340
automorphism?
homologyAbelianization (H1) = C3×C5×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC72×A4×C11⋊C5
unambiguous semidirect productC22⋊(C3×C72×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C72×A4)
unambiguous semidirect product(C11×A4)⋊(C5×C72)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C72)
unambiguous semidirect product(C7×C11×A4)⋊(C5×C7)
unambiguous semidirect product(C72×C11×A4)⋊C5

Splittings

Fitting, socle, HallC22×C72×C11 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C5×C72
HallC22×C72×C11⋊C5 ⋊ C3
HallC72×C11×A4 ⋊ C5
HallC72×C11 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C3×C72
HallC22×C72 ⋊ C3×C11⋊C5
HallC11×A4 ⋊ C5×C72
SylowC11 ⋊ C5×C72×A4
SylowC22 ⋊ C3×C72×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC72A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C5×C72
FrattiniC1G
Fitting, socleC22×C72×C11C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C72

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 313);