Finite Group Databasebeta

C22×#10623010 #15660454

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

Aliases

direct productC22×#10623010

Splittings

FittingC23×C42×C11 ⋊ C2
SylowC11 ⋊ C22×#529

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C42×C11C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC23×C42D11
hypocenterC11C22×#529
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C23×C42

8670 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, 1076249);