Finite Group Databasebeta

C2×#13066523 #14644104

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13066523

Splittings

SylowC11 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC23C11⋊#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#407C2
socleC23×C11#95
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#407D11
hypocenterC11C2×#1305
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 59899);