Finite Group Databasebeta

C22×#10623014 #15660495

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

Aliases

direct productC22×#10623014

Splittings

SylowC11 ⋊ C22×#543

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC23×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11C22×#543
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

9310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

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, 1076290);