Finite Group Databasebeta

#25001818

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #10713

Subgroups

subgroupG/H
center, FrattiniC23×C4C22×D43
commutatorC23×C43C2×C42
FittingC22×#117×C43C2
socleC24×C43C22×C4
prime radicalC25×C43C2×C4
cosocleC23×C4×C43C23
hypercenterC22×#117D43
hypocenterC43#10713
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×#117

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=g,f^2=h,b^a=bd,c^a=ce,i^a=i^42,c^b=ch

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 74789);