Finite Group Databasebeta

#24990561

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

FittingC43×#1850 ⋊ C2
SylowC43 ⋊ #8851

Subgroups

subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1850C2
socleC22×C43#385
prime radicalC22×C22⋊D43C2×C4
cosocleC23×C4×C43C23
hypercenter#1850D43
hypocenterC43#8851
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1850

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=f,f^2=h,b^a=bd,c^a=ce,e^b=eg,d^c=dg,i^c=i^42

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 63532);