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C5×C13×C3⋊#261 #23778561

order10140
isoclinismisoclinic class of C3⋊#261
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C3⋊#261
unambiguous semidirect productC3⋊(C5×C13×#261)

Splittings

Fitting, socle, HallC3×C5×C132 ⋊ C4
derivedC3×C13 ⋊ C4×C5×C13
HallC5×C132 ⋊ Dic3
HallC3×C132 ⋊ C4×C5
SylowC132 ⋊ C5×Dic3
HallC3×C5 ⋊ C13×#261
SylowC3 ⋊ C5×C13×#261

Subgroups

subgroupG/H
center, hypercenterC5×C13C3⋊#261
commutator, hypocenterC3×C13C4×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C132C4
prime radicalC3×C5×C13×D13C2
cosocleC3×D13C2×C5×C13
LCSG ▷ C3×C13
UCSC1 ◁ C5×C13

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13×C9⋊#261, C5×C13×C3⋊AGL(1,𝔽13), C5×C13⋊C3×C3⋊#261, …
maximal normal subgroup ofC5×C13×C3⋊AGL(1,𝔽13), C5×C13⋊C3×C3⋊#261, C5×C3⋊#14523152, …
maximal quotient ofC5×C13×C9⋊#261, C3×C5×C13×C3⋊#261, C5×C13×C3⋊(C3⋊#261)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 219);