Finite Group Databasebeta

#26138235

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

No aliases for this group.

Splittings

FittingC2×C47×#380 ⋊ C2
SylowC47 ⋊ #13877

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#380D47
hypocenterC47#13877
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

4046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 91525);