Finite Group Databasebeta

Dic11×#532 #14912307

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productDic11×#532

Splittings

SylowC11 ⋊ C4×#532

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#532C2
socle, cosocleC23×C11C25
hypercenterC2×#532D11
hypocenterC11C4×#532
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#532

3526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328102);