Finite Group Databasebeta

C2×#13070669 #14908007

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13070669

Splittings

SylowC11 ⋊ C2×#2210

Subgroups

subgroupG/H
centerC23D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC22×C11×D16C2
socleC23×C11C2×D8
hypercenterC22×D16D11
hypocenterC11C2×#2210
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 323802);