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C2×C3×D251⋊C5 #28418906

order15060
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D251⋊C5
unambiguous semidirect productD251⋊(C2×C3×C5)
unambiguous semidirect product(C2×D251)⋊(C3×C5)
unambiguous semidirect product(C251⋊C5)⋊(C22×C3)
unambiguous semidirect product(C2×C251⋊C5)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D251)⋊C5

Splittings

Fitting, socleC2×C3×C251 ⋊ C2×C5
derived, SylowC251 ⋊ C22×C3×C5
HallC3×C251⋊C5 ⋊ C22
HallC2×C3×D251 ⋊ C5
HallC251⋊C5 ⋊ C22×C3
HallC2×D251 ⋊ C3×C5
HallC3×C251 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D251⋊C5
commutator, cosocle, hypocenterC251C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C251C2×C5
LCSG ▷ C251
UCSC1 ◁ C2×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1506

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15060, 16);