Finite Group Databasebeta

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C4⋊C4×C3⋊S4 #11922856

order1152
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC4⋊C4×C3⋊S4

Splittings

FittingC22×C3×C4⋊C4 ⋊ D3

Subgroups

subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
hypercenterC4⋊C4C3⋊S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C4⋊C4

1022 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 115 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) = 144

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 156867);