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C2×C5×#568⋊C3 #14511366

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×#568⋊C3
unambiguous semidirect product(C2×#568)⋊(C3×C5)
unambiguous semidirect product(C2×C5×#568)⋊C3

Splittings

Fitting, HallC2×C5×#568 ⋊ C3
SylowC2×#568 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutator, hypocenterQ8C22×C3×C4×C5
FrattiniC4C23×C5×A4
FittingC2×C5×#568C3
socleC22×C5C2×C4×A4
prime radicalC22×C5×#41⋊C3C2
cosocle#41C23×C3×C5
hypercenterC2×C5×M16A4
LCSG ▷ Q8
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×M16

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237064);