Finite Group Databasebeta

← Prev (#13153550) Next (#13153552) →

C2×#64133⋊C3 #13153551

order1728
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3

Aliases

direct productC2×#64133⋊C3
unambiguous semidirect product(C2×#64133)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C2×C22⋊Q8

Subgroups

subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
FrattiniC22×C3C23×C3×D3
FittingC23×C4×H(3,𝔽3)C2
socleC23×C3C22×C3×D3
prime radicalC24×H(3,𝔽3)C22
hypercenterC23×C4(C3⋊D3)⋊C3
hypocenterC32C2×C3×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

1363 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19614);