Finite Group Databasebeta

C2×#13071910 #14920054

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13071910

Splittings

SylowC11 ⋊ C2×#2399

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
socle, prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#2399
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 335849);