Finite Group Databasebeta

C22×#10623001 #15660479

order2816
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#10623001

Splittings

SylowC11 ⋊ C22×#533

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C42×C11C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C42D11
hypocenterC11C22×#533
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C23×C42

8238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076274);