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C5×C9⋊#4223 #20301551

order7380
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#4223
unambiguous semidirect productC9⋊(C5×#4223)

Splittings

Fitting, HallC5×C9×C41 ⋊ C4
derived, HallC9×C41 ⋊ C4×C5
HallC5×C41 ⋊ Dic9
HallC5×C9 ⋊ #4223
SylowC41 ⋊ C5×Dic9
SylowC9 ⋊ C5×#4223

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#4223
commutator, hypocenterC9×C41C4×C5
FrattiniC3C5×C3⋊#4223
FittingC5×C9×C41C4
socleC3×C5×C41Dic3
LCSG ▷ C9×C41
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

510 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊(#4223⋊C25), C25×C9⋊#4223, C5×C9⋊(#4223⋊C5), …
maximal normal subgroup ofC9⋊(#4223⋊C25), C25×C9⋊#4223, C5×C9⋊(#4223⋊C5), …
maximal quotient ofC25×C9⋊#4223, C52×C9⋊#4223, C5×C9⋊#11717961, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 29);