Finite Group Databasebeta

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C2×#63639⋊C3 #13143111

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

Aliases

direct productC2×#63639⋊C3
unambiguous semidirect product(C2×#63639)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC3×C8C22×C3×D3
FittingC22×C8×H(3,𝔽3)C2
socleC22×C3C2×C3×C3⋊C8
prime radicalC23×H(3,𝔽3)C8
cosocleC32×C8C23×C3
hypercenterC22×C8(C3⋊D3)⋊C3
hypocenterC32C2×C3×M32
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

391 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, 9174);