Finite Group Databasebeta

#26214476

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

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #20470

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#431C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×#431D47
hypocenterC47#20470
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#431

958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167766);