Finite Group Databasebeta

#25095260

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #20521

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC4×C4⋊C8×C43C2
socle, prime radicalC23×C43C23×C4
cosocleC22×C4×C43C24
hypercenterC4×C4⋊C8D43
hypocenterC43#20521
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C8

866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=f,b^2=g,c^2=eg,d^2=ef,f^2=h,b^a=be,c^a=ch,i^a=i^42,c^b=ch,i^b=i^42,d^c=dh,i^d=i^42

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168231);