Finite Group Databasebeta

D31×#444 #16854603

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

Aliases

direct productD31×#444

Splittings

FittingC31×#444 ⋊ C2
SylowC31 ⋊ C2×#444

Subgroups

subgroupG/H
centerC4C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC31×#444C2
socleC2×C31C2×C4×D4
prime radical#135×D31C2
cosocleC2×C4×C31C24
hypercenter#444D31
hypocenterC31C2×#444
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C2×C8 ◁ #444

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 496

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 13402);