Finite Group Databasebeta

C2×#13067390 #14722833

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13067390

Splittings

SylowC11 ⋊ C2×#1571

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC22×C11×C4⋊C8C2
socleC23×C11C2×C4⋊C4
prime radicalC24×C11C4⋊C4
cosocleC42×C11C24
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#1571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 138628);