Finite Group Databasebeta

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C22×C4⋊((C3⋊Dic3)⋊C3) #13153552

order1728
isoclinismisoclinic class of #634⋊C3
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC22×C4⋊((C3⋊Dic3)⋊C3)

Splittings

SylowH(3,𝔽3) ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC23×C4×H(3,𝔽3)C2
socleC24×C3C2×C3×D3
prime radicalC24×H(3,𝔽3)C22
cosocleC22×C32C24×C3
hypercenterC23×C4(C3⋊D3)⋊C3
hypocenterC32C22×C3×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

1699 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19615);