Finite Group Databasebeta

C2×#13067590 #14725957

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13067590

Splittings

SylowC11 ⋊ C2×#1605

Subgroups

subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11C2×#1605
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 141752);