Finite Group Databasebeta

C2×#13070773 #14908388

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

Aliases

direct productC2×#13070773

Splittings

SylowC11 ⋊ C2×#2228

Subgroups

subgroupG/H
centerC23C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C2×D8
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11C2×#2228
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 324183);