Finite Group Databasebeta

#25017983

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C29

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #13794

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC23×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC26×C43C22
hypercenterC23×C22⋊C4D43
hypocenterC43#13794
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=g,c^2=h,b^a=be,c^a=cf,d^a=de,c^b=ce,i^c=i^42

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90954);