Finite Group Databasebeta

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C9×C23×D25 #23780329

order10350
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×D25
unambiguous semidirect productC25⋊(C2×C9×C23)

Splittings

Fitting, HallC9×C23×C25 ⋊ C2
derived, SylowC25 ⋊ C2×C9×C23
HallC23×C25 ⋊ C2×C9
HallC9×C25 ⋊ C2×C23

Subgroups

subgroupG/H
center, hypercenterC9×C23D25
commutator, hypocenterC25C2×C9×C23
FrattiniC3×C5C3×D5×C23
FittingC9×C23×C25C2
socleC3×C5×C23C3×D5
prime radicalC3×C23×D25C3
cosocleC3×C25C2×C3×C23
LCSG ▷ C25
UCSC1 ◁ C9×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2898 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C23×#1035, C9×C23⋊#1035, C23×C9⋊#1035, …
maximal normal subgroup ofC9×C23×#1035, C9×C23⋊#1035, C23×C9⋊#1035, …
maximal quotient ofC9×C23×Dic25, C2×C9×C23×D25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 3);