Finite Group Databasebeta

C2×#14520949 #16848165

order3968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14520949

Splittings

FittingC22×C22⋊C4×C31 ⋊ C2
SylowC31 ⋊ C2×#390

Subgroups

subgroupG/H
centerC24C22×D31
commutatorC22×C31C23×C4
FrattiniC23C23×D31
FittingC22×C22⋊C4×C31C2
socleC24×C31C23
prime radicalC23×C22⋊D31C2
cosocleC23×C31C24
hypercenterC22×C22⋊C4D31
hypocenterC31C2×#390
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 6964);