Finite Group Databasebeta

#25027807

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

No aliases for this group.

Splittings

FittingC43×C22⋊#95 ⋊ C2
SylowC43 ⋊ #14693

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC22⋊#95D43
hypocenterC43#14693
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

6494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=h,b^2=h,b^a=be,c^a=cf,d^a=dg,i^a=i^42,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, 100778);