Finite Group Databasebeta

C2×#13066859 #14675434

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13066859

Splittings

SylowC11 ⋊ C2×#1439

Subgroups

subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC23×C11×C22⋊C4C2
socleC25×C11C23
prime radicalC26×C11C22
cosocleC24×C11C24
hypercenterC23×C22⋊C4D11
hypocenterC11C2×#1439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C22⋊C4

4926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 91229);