Finite Group Databasebeta

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C3×C4×C311⋊C5 #32916207

order18660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C311⋊C5
unambiguous semidirect product(C4×C311)⋊(C3×C5)
unambiguous semidirect product(C3×C4×C311)⋊C5

Splittings

Fitting, HallC3×C4×C311 ⋊ C5
derived, SylowC311 ⋊ C3×C4×C5
HallC4×C311 ⋊ C3×C5
HallC3×C311 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C311⋊C5
commutator, hypocenterC311C3×C4×C5
FrattiniC2C2×C3×C311⋊C5
FittingC3×C4×C311C5
socleC2×C3×C311C2×C5
prime radicalC2×C3×C311⋊C5C2
cosocleC2×C311C2×C3×C5
LCSG ▷ C311
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3732

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18660, 2);