Finite Group Databasebeta

C2×#13066678 #14665138

order2816
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13066678

Splittings

SylowC11 ⋊ C2×#1366

Subgroups

subgroupG/H
centerC22#10622119
commutatorC42×C11C22×C4
FrattiniC4×C8C22×D11
FittingC2×C11×#364C2
socleC22×C11#333
prime radicalC23×C11#100
cosocleC4×C8×C11C23
hypercenterC2×#364D11
hypocenterC11C2×#1366
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 80933);