Finite Group Databasebeta

#25017709

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #13756

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC22⋊#95D43
hypocenterC43#13756
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

3070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90680);