Finite Group Databasebeta

#24987924

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #8298

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC23×C22⋊C4×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC26×C43C4
cosocleC23×C4×C43C23
hypercenterC23×C22⋊C4D43
hypocenterC43#8298
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C22⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^42,f^b=fg

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60895);