Finite Group Databasebeta

C2×#13069643 #14780655

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

Aliases

direct productC2×#13069643

Splittings

SylowC11 ⋊ C2×#2004

Subgroups

subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11#120
hypercenterC2×#535D11
hypocenterC11C2×#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 196450);