Finite Group Databasebeta

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C22⋊C4×C24⋊C5 #13046051

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×C24⋊C5
unambiguous semidirect productC22⋊(C4×C24⋊C5)
unambiguous semidirect product(C24×C22⋊C4)⋊C5

Splittings

Fitting, SylowC24×C22⋊C4 ⋊ C5

Subgroups

subgroupG/H
center, FrattiniC22C22×C24⋊C5
commutatorC25C2×C4×C5
FittingC24×C22⋊C4C5
socle, cosocleC26C22×C5
prime radicalC23×C24⋊C5C2
hypercenterC22⋊C4C24⋊C5
hypocenterC24C5×C22⋊C4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C22 ◁ C22⋊C4

4429 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 4429 conjugacy classes of subgroups — too many to draw. Only its 33 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) = 40

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116319);