Finite Group Databasebeta

C2×#13066437 #14641704

order2816
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13066437

Splittings

SylowC11 ⋊ C2×#1270

Subgroups

subgroupG/H
centerC24C22⋊Dic11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×#390C2
socleC24×C11C22⋊C4
prime radicalC23×D4×C11C4
cosocleC2×C42×C11C23
hypercenterC2×#390D11
hypocenterC11C2×#1270
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 57499);