Finite Group Databasebeta

D31×#367 #16847489

order3968
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD31×#367

Splittings

FittingC31×#367 ⋊ C2
SylowC31 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D31
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC31×#367C2
socleC22×C31C2×D8
prime radicalC22×D31D8
cosocleC2×C8×C31C23
hypercenter#367D31
hypocenterC31C2×#367
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

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, 6288);