Finite Group Databasebeta

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C72×C9×C11⋊C5 #37564682

order24255
automorphism?
homologyAbelianization (H1) = C5×C72×C9 · Schur multiplier (H2) = C7

Aliases

direct productC72×C9×C11⋊C5
unambiguous semidirect productC11⋊(C5×C72×C9)
unambiguous semidirect product(C9×C11)⋊(C5×C72)
unambiguous semidirect product(C7×C9×C11)⋊(C5×C7)
unambiguous semidirect product(C72×C9×C11)⋊C5

Splittings

Fitting, HallC72×C9×C11 ⋊ C5
derived, SylowC11 ⋊ C5×C72×C9
HallC72×C11 ⋊ C5×C9
HallC9×C11 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC72×C9C11⋊C5
commutator, hypocenterC11C5×C72×C9
FrattiniC3C3×C72×C11⋊C5
FittingC72×C9×C11C5
socleC3×C72×C11C3×C5
prime radicalC3×C72×C11⋊C5C3
cosocleC3×C11C3×C5×C72
LCSG ▷ C11
UCSC1 ◁ C72×C9

120 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, 13);