Finite Group Databasebeta

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C3×C4⋊C4×#157 #13173228

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC3×C4⋊C4×#157

Splittings

FittingC33×C4⋊C4 ⋊ C4
SylowC33 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C3C22×#157
commutatorC2×C32C2×C3×C42
FrattiniC22C22×C3×#157
FittingC33×C4⋊C4C4
socleC22×C33C22×C4
prime radicalC22×C3×C3⋊D3C23
cosocleC22×C3⋊D3C23×C3
hypercenterC3×C4⋊C4#157
hypocenterC32C3×C4×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 39291);