Finite Group Databasebeta

C2×#13069790 #14781199

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

Aliases

direct productC2×#13069790

Splittings

SylowC11 ⋊ C2×#2031

Subgroups

subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#410C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenterC2×#410D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

1234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

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, 196994);