Finite Group Databasebeta

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C11×C25×C22⋊C9 #23754757

order9900
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C9×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC11×C25×C22⋊C9
unambiguous semidirect productC22⋊(C9×C11×C25)
unambiguous semidirect product(C22×C25)⋊(C9×C11)
unambiguous semidirect product(C22×C11×C25)⋊C9

Splittings

derived, SylowC22 ⋊ C9×C11×C25
HallC22×C11×C25 ⋊ C9
HallC22×C25 ⋊ C9×C11
HallC22×C11 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C11×C25A4
commutator, hypocenterC22C9×C11×C25
FrattiniC3×C5C5×C11×A4
FittingC22×C3×C11×C25C3
socle, prime radicalC22×C3×C5×C11C3×C5
cosocleC22×C3×C5C3×C5×C11
LCSG ▷ C22
UCSC1 ◁ C3×C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9900, 31);