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C2×(#564⋊C3)⋊C5 #14512433

order1920
isoclinismisoclinic class of (#564⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×(#564⋊C3)⋊C5
unambiguous semidirect product(C2×#564⋊C3)⋊C5
unambiguous semidirect product(C2×#564⋊C5)⋊C3

Splittings

Fitting, SylowC2×#564 ⋊ C3×C5
derived#564 ⋊ C2×C3×C5
HallC2×#564⋊C5 ⋊ C3
HallC2×#564⋊C3 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2(#564⋊C3)⋊C5
commutator, cosocle, hypocenter#564C2×C3×C5
FrattiniC22C2×AGL(1,𝔽16)
FittingC2×#564C3×C5
socleC23AGL(1,𝔽16)
LCSG ▷ #564
UCSC1 ◁ C2

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238131);