Finite Group Databasebeta

← Prev (#13153553) Next (#13153555) →

C22×#3752⋊C3 #13153554

order1728
isoclinismisoclinic class of #634⋊C3
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productC22×#3752⋊C3

Splittings

FittingC23×C4×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC23×C4×H(3,𝔽3)C2
socleC24×C3C2×C3×D3
prime radicalC24×(C3⋊D3)⋊C3C2
cosocleC22×C32C24×C3
hypercenterC23×C4(C3⋊D3)⋊C3
hypocenterC32C22×C3×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

2595 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, 19617);