Finite Group Databasebeta

C2×#13067136 #14720894

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

Aliases

direct productC2×#13067136

Splittings

SylowC11 ⋊ C2×#1508

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#1508
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

1554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 136689);