Finite Group Databasebeta

D11×#1305 #14644101

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD11×#1305

Splittings

FittingC11×#1305 ⋊ C2
SylowC11 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC22D11×#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1305C2
socleC22×C11C2×#95
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1305D11
hypocenterC11C2×#1305
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 59896);