Finite Group Databasebeta

#24987186

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #8167

Subgroups

subgroupG/H
centerC2×C4C2×(C2×D43)⋊C4
commutator, prime radicalC23×C43C2×C42
FrattiniC2×C42C22×D43
FittingC43×#1451C2
socleC22×C43C4×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1451D43
hypocenterC43#8167
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1451

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=e,b^2=f,c^2=eg,e^2=h,f^2=g,b^a=bd,c^a=ch,f^a=fg,i^a=i^42,d^b=dg,i^b=i^42

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60157);