Finite Group Databasebeta

#26137394

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13756

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC23×C42×C47C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC23×C42D47
hypocenterC47#13756
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C23×C42

3070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=g,b^2=h,d^2=f,b^a=be,c^a=cf,i^a=i^46

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90684);