Finite Group Databasebeta

#25017834

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

Aliases

No aliases for this group.

Splittings

FittingC43×#1437 ⋊ C2
SylowC43 ⋊ #13775

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenter#1437D43
hypocenterC43#13775
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

3566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90805);