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C4×(C241⋊C3)⋊C5 #28385990

order14460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C241⋊C3)⋊C5
unambiguous semidirect product(C4×C241⋊C3)⋊C5
unambiguous semidirect product(C4×C241⋊C5)⋊C3

Splittings

Fitting, HallC4×C241 ⋊ C3×C5
derived, SylowC241 ⋊ C3×C4×C5
HallC4×C241⋊C5 ⋊ C3
HallC4×C241⋊C3 ⋊ C5
HallC241⋊C5 ⋊ C3×C4
HallC241⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4(C241⋊C3)⋊C5
commutator, hypocenterC241C3×C4×C5
FrattiniC2C2×(C241⋊C3)⋊C5
FittingC4×C241C3×C5
socle, cosocleC2×C241C2×C3×C5
prime radicalC2×(C241⋊C3)⋊C5C2
LCSG ▷ C241
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14460, 4);