Finite Group Databasebeta

#25018500

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

No aliases for this group.

Splittings

FittingC23×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ #13872

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC23×C4⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC23×C4⋊C4D43
hypocenterC43#13872
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4⋊C4

2950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 91471);