Finite Group Databasebeta

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C5×C3⋊#14559075 #49137415

order36300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productC5×C3⋊#14559075
unambiguous semidirect productC3⋊(C5×#14559075)

Splittings

Fitting, socleC3×C5×C112 ⋊ Dic5
derivedC3×#10597245 ⋊ C4×C5
HallC3×C5×#10597245 ⋊ C4
HallC5×#10597245 ⋊ Dic3
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C5×Dic15
SylowC3 ⋊ C5×#14559075

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#14559075
commutator, hypocenterC3×#10597245C4×C5
FrattiniC1G
Fitting, socleC3×C5×C112Dic5
prime radicalC3×C5×#11925893C2
cosocleC3×#11925893C2×C5
LCSG ▷ C3×#10597245
UCSC1 ◁ C5

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 551);