Finite Group Databasebeta

#123×Dic31 #16848234

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#123×Dic31

Splittings

SylowC31 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC2×C31×#123C2
socle, cosocleC23×C31C24
prime radicalC22×D4×C31C22
hypercenterC2×#123D31
hypocenterC31C4×#123
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#123

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 7033);