Finite Group Databasebeta

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C2×C5×A4×M16 #14511363

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

Aliases

direct productC2×C5×A4×M16
unambiguous semidirect product(C23×M16)⋊(C3×C5)
unambiguous semidirect product(C23×C5×M16)⋊C3

Splittings

Fitting, HallC23×C5×M16 ⋊ C3
SylowC23×M16 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC4C23×C5×A4
FittingC23×C5×M16C3
socleC24×C5C2×C3×C4
prime radicalC23×C5×A4C4
cosocleC22×C4C23×C3×C5
hypercenterC2×C5×M16A4
hypocenterC22C2×C3×C5×M16
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×M16

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237061);