Finite Group Databasebeta

#24993408

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

FittingC43×#2875 ⋊ C2
SylowC43 ⋊ #9311

Subgroups

subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2875C2
socleC22×C43#386
prime radical#19144746C2
cosocleC2×C42×C43C23
hypercenter#2875D43
hypocenterC43#9311
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2875

514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=df,d^2=gh,e^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^42,d^b=dh,f^b=fh,e^c=eh

Conjugacy classes & character table

1477 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 66379);