Finite Group Databasebeta

C2×#13070262 #14906500

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

Aliases

direct productC2×#13070262

Splittings

SylowC11 ⋊ C2×#2121

Subgroups

subgroupG/H
centerC22C2×#66898
commutatorC23×C11C23×C4
FrattiniC2×D4C23×D11
Fitting, prime radicalC2×C11×#534C2
socleC22×C11C2×#99
cosocleC2×D4×C11C24
hypercenterC2×#534D11
hypocenterC11C2×#2121
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#534

1494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

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, 322295);