Finite Group Databasebeta

D31×#431 #16854323

order3968
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productD31×#431

Splittings

FittingC31×#431 ⋊ C2
SylowC31 ⋊ C2×#431

Subgroups

subgroupG/H
centerC42C22×D31
commutatorC2×C31C23×C8
FrattiniC2×C4C23×D31
FittingC31×#431C2
socleC22×C31C23×C4
prime radicalC23×D31C2×C4
cosocleC2×C4×C31C24
hypercenter#431D31
hypocenterC31C2×#431
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C42 ◁ #431

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13122);