Finite Group Databasebeta

D31×#344 #16845451

order3968
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD31×#344

Splittings

FittingC31×#344 ⋊ C2
SylowC31 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D31
commutatorC22×C31C2×C42
FrattiniC22×C4C22×D31
FittingC31×#344C2
socleC2×C31C2×#95
prime radicalC23×D31C2×C4
cosocleC22×C4×C31C23
hypercenter#344D31
hypocenterC31C2×#344
LCSG ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 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, 4250);