Finite Group Databasebeta

C2×#13069226 #14756054

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13069226

Splittings

SylowC11 ⋊ C2×#1924

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C22×C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#1924
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 171849);