Finite Group Databasebeta

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C9×C49×C11⋊C5 #37564672

order24255
automorphism?
homologyAbelianization (H1) = C5×C9×C49 · Schur multiplier (H2) = C1

Aliases

direct productC9×C49×C11⋊C5
unambiguous semidirect productC11⋊(C5×C9×C49)
unambiguous semidirect product(C9×C11)⋊(C5×C49)
unambiguous semidirect product(C9×C11×C49)⋊C5

Splittings

Fitting, HallC9×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C5×C9×C49
HallC11×C49 ⋊ C5×C9
HallC9×C11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC9×C49C11⋊C5
commutator, hypocenterC11C5×C9×C49
FrattiniC3×C7C3×C7×C11⋊C5
FittingC9×C11×C49C5
socle, cosocleC3×C7×C11C3×C5×C7
prime radicalC3×C7×C11⋊C5C3×C7
LCSG ▷ C11
UCSC1 ◁ C9×C49

36 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, 3);