Finite Group Databasebeta

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C13×C25×Dic9 #26043162

order11700
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C4×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25×Dic9
unambiguous semidirect productC9⋊(C4×C13×C25)

Splittings

derived, SylowC9 ⋊ C4×C13×C25
HallC9×C13×C25 ⋊ C4
HallC9×C25 ⋊ C4×C13
HallC9×C13 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C13×C25D9
commutator, hypocenterC9C4×C13×C25
FrattiniC2×C3×C5C5×D3×C13
FittingC2×C9×C13×C25C2
socle, prime radicalC2×C3×C5×C13C5×D3
cosocleC2×C5×C9C2×C5×C13
LCSG ▷ C9
UCSC1 ◁ C2×C13×C25

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 9);