Finite Group Databasebeta

C22×#10622729 #15620871

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

Aliases

direct productC22×#10622729

Splittings

SylowC11 ⋊ C22×#467

Subgroups

subgroupG/H
centerC24C2×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC24×C8×C11C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC24×C8D11
hypocenterC11C22×#467
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C24×C8

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1036666);