Finite Group Databasebeta

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C4×#3748⋊C3 #13142408

order1728
isoclinismisoclinic class of #634⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C3×C4

Aliases

direct productC4×#3748⋊C3
unambiguous semidirect product(C4×#3748)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C4×M16

Subgroups

subgroupG/H
centerC42C2×(C3⋊D3)⋊C3
commutatorC2×C32C2×C3×C42
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C42×H(3,𝔽3)C2
socleC22×C3C22×C3×Dic3
prime radicalC23×H(3,𝔽3)C2×C4
cosocleC2×C32×C4C23×C3
hypercenterC2×C42(C3⋊D3)⋊C3
hypocenterC32C3×C4×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

605 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 8471);