Finite Group Databasebeta

C2×#14521845 #16860454

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14521845

Splittings

FittingC2×C31×AGL(1,ℤ/8) ⋊ C2
SylowC31 ⋊ C2×#575

Subgroups

subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC4×C31C25
FrattiniC4C24×D31
FittingC2×C31×AGL(1,ℤ/8)C2
socleC22×C31C22×D4
hypercenterC2×AGL(1,ℤ/8)D31
hypocenterC31C2×#575
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 992

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, 19253);