Finite Group Databasebeta

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C2×C9×C11×D25 #23754759

order9900
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C11×D25
unambiguous semidirect productC25⋊(C22×C9×C11)
unambiguous semidirect product(C2×C25)⋊(C2×C9×C11)

Splittings

FittingC2×C9×C11×C25 ⋊ C2
derived, SylowC25 ⋊ C22×C9×C11
HallC9×C11×C25 ⋊ C22
HallC11×C25 ⋊ C22×C9
HallC9×C25 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D25
commutator, hypocenterC25C22×C9×C11
FrattiniC3×C5C2×C3×D5×C11
FittingC2×C9×C11×C25C2
socleC2×C3×C5×C11C3×D5
prime radicalC2×C3×C11×D25C3
cosocleC3×C25C22×C3×C11
LCSG ▷ C25
UCSC1 ◁ C2×C9×C11

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9900, 33);