Finite Group Databasebeta

C22×#10622121 #14720114

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#10622121

Splittings

FittingC22×C11×C4⋊C8 ⋊ C2
SylowC11 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC22×C11×C4⋊C8C2
socleC24×C11C22⋊C4
prime radicalC23×D44C4
cosocleC42×C11C24
hypercenterC22×C4⋊C8D11
hypocenterC11C22×D4⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 135909);