Finite Group Databasebeta

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C3×#14559031⋊C5 #49136559

order36270
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×#14559031⋊C5
unambiguous semidirect product(C3×#14559031)⋊C5

Splittings

Fitting, socleC3×C13×C31 ⋊ C2×C3×C5
derived, HallC13×C31 ⋊ C2×C32×C5
HallC3×#11925881⋊C5 ⋊ C2
HallC3×#14559031 ⋊ C5
HallC13⋊(D31⋊C5) ⋊ C32
HallC3×#11925881 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C32
HallD403 ⋊ C32×C5
HallΓL(1,𝔽32) ⋊ C3×D13⋊C3
SylowC31 ⋊ C3×C5×D13⋊C3
SylowC13 ⋊ C3×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC3#14559031⋊C5
commutator, cosocle, hypocenterC13×C31C2×C32×C5
FrattiniC1G
Fitting, socleC3×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 79);