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C2×C5×A4×C16 #14510997

order1920
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×A4×C16
unambiguous semidirect product(C23×C16)⋊(C3×C5)
unambiguous semidirect product(C23×C5×C16)⋊C3

Splittings

Fitting, HallC23×C5×C16 ⋊ C3
derivedC22 ⋊ C2×C3×C5×C16
SylowC23×C16 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C16A4
commutator, hypocenterC22C2×C3×C5×C16
FrattiniC8C22×C5×A4
FittingC23×C5×C16C3
socleC24×C5C3×C8
prime radicalC22×C5×A4C8
cosocleC22×C8C22×C3×C5
LCSG ▷ C22
UCSC1 ◁ C2×C5×C16

240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 480

Conjugacy classes & character table

640 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236695);