Finite Group Databasebeta

#25017678

order11008
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

No aliases for this group.

Splittings

FittingC4×#95×C43 ⋊ C2
SylowC43 ⋊ #13749

Subgroups

subgroupG/H
center, FrattiniC24C23×D43
commutatorC2×C43C2×C43
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#13749
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

2598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=g,c^2=h,b^a=be,d^a=de,c^b=ce,i^d=i^42

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 90649);