Finite Group Databasebeta

C2×#13071681 #14913373

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13071681

Splittings

SylowC11 ⋊ C2×#2366

Subgroups

subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#127C2
socleC24×C11C24
cosocleC23×C11C25
hypercenterC22×#127D11
hypocenterC11C2×#2366
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#127

5062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 329168);