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C9×D5×C132 #29503595

order15210
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C9×C132 · Schur multiplier (H2) = C13

Aliases

direct productC9×D5×C132
unambiguous semidirect productC5⋊(C2×C9×C132)

Splittings

Fitting, HallC5×C9×C132 ⋊ C2
derived, SylowC5 ⋊ C2×C9×C132
HallC5×C132 ⋊ C2×C9
HallC5×C9 ⋊ C2×C132

Subgroups

subgroupG/H
center, hypercenterC9×C132D5
commutator, hypocenterC5C2×C9×C132
FrattiniC3C3×D5×C132
FittingC5×C9×C132C2
socleC3×C5×C132C2×C3
prime radicalC3×D5×C132C3
cosocleC3×C5C2×C3×C132
LCSG ▷ C5
UCSC1 ◁ C9×C132

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7605

Conjugacy classes & character table

6084 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C132×AGL(1,𝔽5), C9×C13×#63120, C9×#16810007, …
maximal normal subgroup ofC9×C132×AGL(1,𝔽5), C9×C13×#63120, C9×#16810007, …
maximal quotient ofC9×C132×Dic5, C2×C9×D5×C132

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 58);