Finite Group Databasebeta

#731×C127⋊C3 #44525093

order30861
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct product#731×C127⋊C3

Splittings

Fitting#731×C127 ⋊ C3
SylowC127 ⋊ C3×#731

Subgroups

subgroupG/H
centerC3H(3,𝔽3)×C127⋊C3
commutator, cosocleC32×C127C33
FrattiniC32C32×C127⋊C3
Fitting#731×C127C3
socleC3×C127C3×H(3,𝔽3)
prime radicalH(3,𝔽3)×C127⋊C3C3
hypercenter#731C127⋊C3
hypocenterC127C3×#731
LCSG ▷ C32×C127 ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ C32 ◁ #731

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Conjugacy classes & character table

765 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 247);