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C2×C3×(C271⋊C3)⋊C5 #37567269

order24390
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C271⋊C3)⋊C5
unambiguous semidirect product(C2×C271⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C271⋊C5)⋊C32
unambiguous semidirect product(C2×C3×C271⋊C3)⋊C5
unambiguous semidirect product(C2×C3×C271⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C271 ⋊ C3×C5
derived, SylowC271 ⋊ C2×C32×C5
HallC2×C3×C271⋊C3 ⋊ C5
HallC2×C271⋊C5 ⋊ C32
HallC3×C271⋊C3 ⋊ C2×C5
HallC271⋊C5 ⋊ C2×C32
HallC2×C271 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(C271⋊C3)⋊C5
commutator, cosocle, hypocenterC271C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C271C3×C5
LCSG ▷ C271
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1626

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24390, 28);