Finite Group Databasebeta

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C4×C5×C409⋊C3 #37589330

order24540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C409⋊C3
unambiguous semidirect product(C4×C409)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C409)⋊C3

Splittings

Fitting, HallC4×C5×C409 ⋊ C3
derived, SylowC409 ⋊ C3×C4×C5
HallC5×C409 ⋊ C3×C4
HallC4×C409 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C409⋊C3
commutator, hypocenterC409C3×C4×C5
FrattiniC2C2×C5×C409⋊C3
FittingC4×C5×C409C3
socleC2×C5×C409C2×C3
prime radicalC2×C5×C409⋊C3C2
cosocleC2×C409C2×C3×C5
LCSG ▷ C409
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8180

Conjugacy classes & character table

2780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24540, 2);