Finite Group Databasebeta

C2×#13066494 #14643756

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13066494

Splittings

SylowC11 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#380C2
socleC24×C11C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#1294
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 59551);