Finite Group Databasebeta

C2×#13071861 #14920000

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13071861

Splittings

FittingC2×C11×#396 ⋊ C2
SylowC11 ⋊ C2×#2392

Subgroups

subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#396D11
hypocenterC11C2×#2392
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

4134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 335795);