Finite Group Databasebeta

D7×#733 #11765657

order1134
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productD7×#733

Splittings

Fitting, HallC7×#733 ⋊ C2
SylowC7 ⋊ C2×#733

Subgroups

subgroupG/H
centerC3D7×H(3,𝔽3)
commutator, cosocleC32×C7C2×C32
FrattiniC32C32×D7
FittingC7×#733C2
socleC3×C7C2×H(3,𝔽3)
prime radicalC32×D7C32
hypercenter#733D7
hypocenterC7C2×#733
LCSG ▷ C32×C7 ▷ C3×C7 ▷ C7
UCSC1 ◁ C3 ◁ C32 ◁ #733

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 189

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 87);