Finite Group Databasebeta

C2×#13070190 #14783737

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

Aliases

direct productC2×#13070190

Splittings

SylowC11 ⋊ C2×#2102

Subgroups

subgroupG/H
centerC2×C4#66989
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC22×C11#400
prime radicalC24×C11#41
hypercenterC2×#430D11
hypocenterC11C2×#2102
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

710 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, 199532);