Finite Group Databasebeta

C2×#13070586 #14907703

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

Aliases

direct productC2×#13070586

Splittings

FittingC22×C11×SD32 ⋊ C2
SylowC11 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#10622769
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×SD32C2
socleC22×C11#447
prime radicalC2×#10623288C2
hypercenterC22×SD32D11
hypocenterC11C2×#2194
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

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, 323498);