Finite Group Databasebeta

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C32×C72×C11⋊C5 #37564692

order24255
automorphism?
homologyAbelianization (H1) = C32×C5×C72 · Schur multiplier (H2) = C3×C7

Aliases

direct productC32×C72×C11⋊C5
unambiguous semidirect productC11⋊(C32×C5×C72)
unambiguous semidirect product(C3×C11)⋊(C3×C5×C72)
unambiguous semidirect product(C32×C11)⋊(C5×C72)
unambiguous semidirect product(C32×C7×C11)⋊(C5×C7)
unambiguous semidirect product(C32×C72×C11)⋊C5

Splittings

Fitting, socle, HallC32×C72×C11 ⋊ C5
derived, SylowC11 ⋊ C32×C5×C72
HallC72×C11 ⋊ C32×C5
HallC32×C11 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC32×C72C11⋊C5
commutator, cosocle, hypocenterC11C32×C5×C72
FrattiniC1G
Fitting, socleC32×C72×C11C5
LCSG ▷ C11
UCSC1 ◁ C32×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4851

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 23);