Finite Group Databasebeta

C2×Dic2096 #30668266

order16768
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic2096

Splittings

SylowC131 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D2096
commutator, cosocleC16×C131C23
FrattiniC16C22×D131
FittingC2×C32×C131C2
socle, prime radicalC22×C131D16
hypercenterC2×C32D131
hypocenterC131C2×Q64
LCSG ▷ C16×C131 ▷ C8×C131 ▷ C4×C131 ▷ C2×C131 ▷ C131
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16768

Conjugacy classes & character table

4198 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16768, 6815);