Finite Group Databasebeta

C2×#13066943 #14719610

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13066943

Splittings

SylowC11 ⋊ C2×#1462

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC23×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC26×C11C4
cosocleC22×C4×C11C24
hypercenterC23×C22⋊C4D11
hypocenterC11C2×#1462
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C22⋊C4

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 135405);