Finite Group Databasebeta

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C5×C3⋊(#92150⋊C5) #49137416

order36300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C3⋊(#92150⋊C5)
unambiguous semidirect productC3⋊(C5×#92150⋊C5)
unambiguous semidirect product(C3⋊#92150)⋊C52
unambiguous semidirect product(C5×C3⋊#92150)⋊C5

Splittings

Fitting, socleC3×C5×C112 ⋊ C4×C5
derived, HallC3×C112 ⋊ C4×C52
HallC3×C5×#10597243 ⋊ C4
HallC5×#10597243 ⋊ Dic3
HallC3⋊#92150 ⋊ C52
SylowC112 ⋊ C52×Dic3
SylowC3 ⋊ C5×#92150⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(#92150⋊C5)
commutator, hypocenterC3×C112C4×C52
FrattiniC1G
Fitting, socleC3×C5×C112C4×C5
prime radicalC3×C5×#11925892C2
cosocleC3×C11⋊D11C2×C52
LCSG ▷ C3×C112
UCSC1 ◁ C5

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 552);