Finite Group Databasebeta

#24987020

order11008
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C43

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #8131

Subgroups

subgroupG/H
centerC43C2×D43
commutatorC2×C43C2×C82
FrattiniC2×C42C22×D43
FittingC42×C8×C43C2
socle, prime radicalC23×C43C2×C42
cosocleC2×C42×C43C23
hypercenterC42×C8D43
hypocenterC43#8131
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C43 ◁ C42×C8

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 59991);