Finite Group Databasebeta

D31×#418 #16854209

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

Aliases

direct productD31×#418

Splittings

FittingC31×#418 ⋊ C2
SylowC31 ⋊ C2×#418

Subgroups

subgroupG/H
centerC22C2×D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC31×#418C2
socleC22×C31C22×D4
prime radicalC22×D4×D31C2
cosocleC2×C4×C31C24
hypercenter#418D31
hypocenterC31C2×#418
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

1008 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, 13008);