Finite Group Databasebeta

C2×#13070587 #14907704

order2816
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13070587

Splittings

SylowC11 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#10622830
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#576C2
socleC22×C11#447
hypercenterC2×#576D11
hypocenterC11C2×#2194
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#576

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 323499);