Finite Group Databasebeta

C2×#13067432 #14723163

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13067432

Splittings

SylowC11 ⋊ C2×#1579

Subgroups

subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socle, prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1579
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 138958);