Finite Group Databasebeta

Dic11×#550 #14913630

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

Aliases

direct productDic11×#550

Splittings

SylowC11 ⋊ C4×#550

Subgroups

subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#550C2
socle, cosocleC23×C11C25
hypercenterC2×#550D11
hypocenterC11C4×#550
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#550

3420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 329425);