Finite Group Databasebeta

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C2×C5×A4×SD16 #14511369

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

Aliases

direct productC2×C5×A4×SD16
unambiguous semidirect product(C23×SD16)⋊(C3×C5)
unambiguous semidirect product(C23×C5×SD16)⋊C3

Splittings

Fitting, HallC23×C5×SD16 ⋊ C3
SylowC23×SD16 ⋊ C3×C5

Subgroups

subgroupG/H
centerC22×C5D4×A4
commutator, cosocleC22×C4C23×C3×C5
FrattiniC4C23×C5×A4
FittingC23×C5×SD16C3
socleC24×C5C3×D4
prime radicalC2×C5×D4×A4C2
hypercenterC2×C5×SD16A4
hypocenterC22C2×C3×C5×SD16
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×SD16

800 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237067);