Finite Group Databasebeta

C2×#13071291 #14912508

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13071291

Splittings

SylowC11 ⋊ C2×#2323

Subgroups

subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2323
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

3198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328303);