Finite Group Databasebeta

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C3×C4×C401⋊C5 #37562609

order24060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C401⋊C5
unambiguous semidirect product(C4×C401)⋊(C3×C5)
unambiguous semidirect product(C3×C4×C401)⋊C5

Splittings

Fitting, HallC3×C4×C401 ⋊ C5
derived, SylowC401 ⋊ C3×C4×C5
HallC4×C401 ⋊ C3×C5
HallC3×C401 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C401⋊C5
commutator, hypocenterC401C3×C4×C5
FrattiniC2C2×C3×C401⋊C5
FittingC3×C4×C401C5
socleC2×C3×C401C2×C5
prime radicalC2×C3×C401⋊C5C2
cosocleC2×C401C2×C3×C5
LCSG ▷ C401
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4812

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24060, 2);