Finite Group Databasebeta

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C2×#63647⋊C3 #13143123

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C24×C3

Aliases

direct productC2×#63647⋊C3
unambiguous semidirect product(C2×#63647)⋊C3

Splittings

FittingC22×C8×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C8×H(3,𝔽3)C2
socleC23×C3C3×C4×D3
prime radicalC23×(C3⋊D3)⋊C3C4
cosocleC2×C32×C4C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C2×C3×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

783 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, 9186);