Finite Group Databasebeta

C22×#10622090 #14720854

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#10622090

Splittings

SylowC11 ⋊ C22×#328

Subgroups

subgroupG/H
centerC24(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#95C2
socleC24×C11C22⋊C4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×#95D11
hypocenterC11C22×#328
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#95

1846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 136649);