Finite Group Databasebeta

C2×#14521517 #16858890

order3968
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14521517

Splittings

FittingC2×C31×#117 ⋊ C2
SylowC31 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutatorC2×C31C24×C4
FrattiniC22C24×D31
FittingC2×C31×#117C2
socleC23×C31C24
prime radicalC22×#92495C2
cosocleC22×C31C25
hypercenterC2×#117D31
hypocenterC31C2×C4×#41
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×#117

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17689);