Finite Group Databasebeta

C2×#14521581 #16858975

order3968
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14521581

Splittings

FittingC2×C4×D4×C31 ⋊ C2
SylowC31 ⋊ C2×#529

Subgroups

subgroupG/H
centerC22×C4C22×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C4×D4×C31C2
socleC23×C31C24
prime radicalC2×#11758515C2
hypercenterC2×C4×D4D31
hypocenterC31C2×#529
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

1232 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, 17774);