Finite Group Databasebeta

#26138147

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

No aliases for this group.

Splittings

FittingC47×C22⋊#95 ⋊ C2
SylowC47 ⋊ #13867

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C22⋊#95C2
socle, cosocleC24×C47C24
prime radicalC24×D188C2
hypercenterC22⋊#95D47
hypocenterC47#13867
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22⋊#95

7150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,i^b=i^46,i^c=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, 91437);