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C3×C5×C3⋊#261 #14556804

order2340
isoclinismisoclinic class of C3⋊#261
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C3⋊#261
unambiguous semidirect productC3⋊(C3×C5×#261)

Splittings

Fitting, socle, HallC32×C5×C13 ⋊ C4
derivedC3×C13 ⋊ C3×C4×C5
HallC32×C13 ⋊ C4×C5
HallC5×C13 ⋊ C3×Dic3
HallC32×C5 ⋊ #261
SylowC13 ⋊ C3×C5×Dic3
SylowC32 ⋊ C5×#261

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#261
commutator, hypocenterC3×C13C3×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C13C4
prime radicalC32×C5×D13C2
cosocleC3×D13C2×C3×C5
LCSG ▷ C3×C13
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 390

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C25×C3⋊#261, C3×C52×C3⋊#261, C3×C5×C3⋊#63122, …
maximal normal subgroup ofC3×C25×C3⋊#261, C3×C52×C3⋊#261, C3×C5×C7×C3⋊#261, …
maximal quotient ofC3×C25×C3⋊#261, C3×C52×C3⋊#261, C3×C5×C3⋊#63122, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 108);