Finite Group Databasebeta

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C5×C3⋊#14559102 #49137746

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

Aliases

direct productC5×C3⋊#14559102
unambiguous semidirect productC3⋊(C5×#14559102)

Splittings

Fitting, socle, HallC3×C52×C112 ⋊ C4
derivedC3×C5×C112 ⋊ C4×C5
HallC52×C112 ⋊ Dic3
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C5×Dic15
HallC3×C52 ⋊ #92150
SylowC52 ⋊ C3⋊#92150
SylowC3 ⋊ C5×#14559102

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#14559102
commutator, hypocenterC3×C5×C112C4×C5
FrattiniC1G
Fitting, socleC3×C52×C112C4
prime radicalC3×C52×C11⋊D11C2
cosocleC3×C5×C11⋊D11C2×C5
LCSG ▷ C3×C5×C112
UCSC1 ◁ C5

256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 882);