Finite Group Databasebeta

C22×#10622596 #14919984

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#10622596

Splittings

SylowC11 ⋊ C22×#398

Subgroups

subgroupG/H
centerC25C22×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC23×C11×C4⋊C4C2
socle, prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11C22×#398
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C4⋊C4

4158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 335779);