Finite Group Databasebeta

C2×#13069619 #14780563

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13069619

Splittings

SylowC11 ⋊ C2×#2000

Subgroups

subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C2×D4
hypercenterC22×#121D11
hypocenterC11C2×#2000
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

2526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 196358);