Finite Group Databasebeta

#737×C127⋊C3 #44525146

order30861
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct product#737×C127⋊C3

Splittings

Fitting#737×C127 ⋊ C3
SylowC127 ⋊ C3×#737

Subgroups

subgroupG/H
centerC9C32×C127⋊C3
commutator, socle, cosocleC3×C127C34
FrattiniC3C33×C127⋊C3
Fitting#737×C127C3
prime radicalH(3,𝔽3)×C127⋊C3C3
hypercenter#737C127⋊C3
hypocenterC127C3×#737
LCSG ▷ C3×C127 ▷ C127
UCSC1 ◁ C9 ◁ #737

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 300);