Finite Group Databasebeta

C2×#13068030 #14736147

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

Aliases

direct productC2×#13068030

Splittings

SylowC11 ⋊ C2×#1678

Subgroups

subgroupG/H
centerC23#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC23×C11#121
prime radicalC2×C11×#127C22
hypercenterC2×#460D11
hypocenterC11C2×#1678
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 151942);