Finite Group Databasebeta

← Prev (#13141608) Next (#13141610) →

C22⋊C8×(C3⋊D3)⋊C3 #13141609

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

Aliases

direct productC22⋊C8×(C3⋊D3)⋊C3
unambiguous semidirect product(C3⋊D3×C22⋊C8)⋊C3

Splittings

FittingH(3,𝔽3)×C22⋊C8 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4C22×(C3⋊D3)⋊C3
commutatorC2×C32C22×C3×C8
FrattiniC2×C3×C4C22×C3×D3
FittingH(3,𝔽3)×C22⋊C8C2
socleC22×C3C2×C3×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 ◁ C2×C4 ◁ C22⋊C8

757 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7672);