Finite Group Databasebeta

C2×#13066711 #14668665

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

Aliases

direct productC2×#13066711

Splittings

SylowC11 ⋊ C2×#1382

Subgroups

subgroupG/H
centerC22×C4#4323
commutatorC8×C11C2×C42
FrattiniC22×C8C22×D11
FittingC2×C11×#427C2
socleC23×C11#102
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#427D11
hypocenterC11C2×#1382
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84460);