Finite Group Databasebeta

C2×#13077500 #15617937

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13077500

Splittings

SylowC11 ⋊ C2×#2952

Subgroups

subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
Fitting, prime radicalC22×C11×#135C2
socleC23×C11C22×D4
cosocleC2×C4×C11C25
hypercenterC22×#135D11
hypocenterC11C2×#2952
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033732);