Finite Group Databasebeta

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C2×#64081⋊C3 #13152302

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C24×C3×C4

Aliases

direct productC2×#64081⋊C3
unambiguous semidirect product(C2×#64081)⋊C3

Splittings

FittingC2×C42×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC2×C42×H(3,𝔽3)C2
socleC23×C3C22×C3×D3
prime radicalC23×(C3⋊D3)⋊C3C22
cosocleC22×C32C24×C3
hypercenterC2×C42(C3⋊D3)⋊C3
hypocenterC32C2×C3×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

1263 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, 18365);