Finite Group Databasebeta

#25259459

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

No aliases for this group.

Splittings

SylowC43 ⋊ #34369

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
Fitting, prime radicalC2×C43×#532C2
socle, cosocleC23×C43C25
hypercenterC2×#532D43
hypocenterC43#34369
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#532

2410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|a^2=h,c^2=fg,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^42,c^b=cg,d^b=df

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 332430);