Finite Group Databasebeta

C2×#13070627 #14907814

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

Aliases

direct productC2×#13070627

Splittings

SylowC11 ⋊ C2×#2201

Subgroups

subgroupG/H
centerC22#10622645
commutator, cosocleC2×D4×C11C24
FrattiniC2×D4C23×D11
FittingC2×C11×#458C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×H(5,𝔽2)C22
hypercenterC2×#458D11
hypocenterC11C2×#2201
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

194 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 323609);