Finite Group Databasebeta

#25260056

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

No aliases for this group.

Splittings

FittingC43×#2374 ⋊ C2
SylowC43 ⋊ #34412

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2374C2
socle, cosocleC23×C43C25
prime radicalC22×#10621900C22
hypercenter#2374D43
hypocenterC43#34412
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2374

2286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=h,b^2=f,c^2=fh,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^e=i^42

Conjugacy classes & character table

1126 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 333027);