Finite Group Databasebeta

#25022978

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

FittingC43×#1440 ⋊ C2
SylowC43 ⋊ #14259

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1440C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1440D43
hypocenterC43#14259
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1440

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 95949);