Finite Group Databasebeta

#25017694

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

Aliases

No aliases for this group.

Splittings

FittingC2×C43×#376 ⋊ C2
SylowC43 ⋊ #13753

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C22×C42
FrattiniC24C23×D43
FittingC2×C43×#376C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC2×#376D43
hypocenterC43#13753
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×#376

2638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90665);