Finite Group Databasebeta

C2×#13070785 #14908501

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13070785

Splittings

SylowC11 ⋊ C2×#2230

Subgroups

subgroupG/H
centerC22#10622374
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#360C2
socleC22×C11#476
prime radicalC2×C11×#135C22
hypercenterC2×#360D11
hypocenterC11C2×#2230
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

206 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 324296);