Finite Group Databasebeta

C2×#13070129 #14782890

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

Aliases

direct productC2×#13070129

Splittings

SylowC11 ⋊ C2×#2090

Subgroups

subgroupG/H
centerC23#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11#121
prime radicalC24×C11#41
hypercenterC2×#428D11
hypocenterC11C2×#2090
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 198685);