Finite Group Databasebeta

C22×#10622703 #15620572

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

Aliases

direct productC22×#10622703

Splittings

SylowC11 ⋊ C22×#462

Subgroups

subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C4⋊Q8C2
socle, prime radicalC24×C11C2×D4
hypercenterC22×C4⋊Q8D11
hypocenterC11C22×#462
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1036367);