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C3×C5×C3⋊#4223 #20301615

order7380
isoclinismisoclinic class of C3⋊#4223
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C3⋊#4223
unambiguous semidirect productC3⋊(C3×C5×#4223)

Splittings

Fitting, socle, HallC32×C5×C41 ⋊ C4
derivedC3×C41 ⋊ C3×C4×C5
HallC32×C41 ⋊ C4×C5
HallC5×C41 ⋊ C3×Dic3
HallC32×C5 ⋊ #4223
SylowC41 ⋊ C3×C5×Dic3
SylowC32 ⋊ C5×#4223

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#4223
commutator, hypocenterC3×C41C3×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C41C4
LCSG ▷ C3×C41
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

540 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C3⋊(#4223⋊C25), C3×C25×C3⋊#4223, C3×C5×C3⋊(#4223⋊C5), …
maximal normal subgroup ofC3×C3⋊(#4223⋊C25), C3×C25×C3⋊#4223, C3×C5×C3⋊(#4223⋊C5), …
maximal quotient ofC3×C25×C3⋊#4223, C3×C52×C3⋊#4223, C3×C5×C3⋊#11717964, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 93);