Finite Group Databasebeta

C2×D992 #16848009

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

Aliases

direct productC2×D992

Splittings

FittingC2×C31×C32 ⋊ C2
SylowC31 ⋊ C2×D32

Subgroups

subgroupG/H
centerC22D496
commutator, cosocleC16×C31C23
FrattiniC16C22×D31
FittingC2×C31×C32C2
socleC22×C31D16
hypercenterC2×C32D31
hypocenterC31C2×D32
LCSG ▷ C16×C31 ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1984

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 6808);