Finite Group Databasebeta

C2×#13077211 #15617440

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

Aliases

direct productC2×#13077211

Splittings

SylowC11 ⋊ C2×#2912

Subgroups

subgroupG/H
centerC23C22×D44
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×#131C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC22×#131D11
hypocenterC11C2×#2912
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#131

2766 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, 1033235);