Finite Group Databasebeta

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C22×D9×S4 #13180051

order1728
isoclinismisoclinic class of D9×S4
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC22×D9×S4
unambiguous semidirect product(C9×S4)⋊C23
unambiguous semidirect product(C9⋊S4)⋊C23
unambiguous semidirect product(A4×D9)⋊C23

Splittings

FittingC24×C9 ⋊ C2×D3
derivedC9×A4 ⋊ C24

Subgroups

subgroupG/H
center, hypercenterC22D9×S4
commutator, cosocle, hypocenterC9×A4C24
FrattiniC3C22×D3×S4
FittingC24×C9C2×D3
socleC24×C3D32
LCSG ▷ C9×A4
UCSC1 ◁ C22

2167 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 2167 conjugacy classes of subgroups — too many to draw. Only its 151 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) = 108

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46114);