Finite Group Databasebeta

D31×#472 #16855414

order3968
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD31×#472

Splittings

FittingC31×#472 ⋊ C2
SylowC31 ⋊ C2×#472

Subgroups

subgroupG/H
centerC2#121×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#472C2
socleC2×C31C2×#121
hypercenter#472D31
hypocenterC31C2×#472
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 496

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 14213);