Finite Group Databasebeta

#26138010

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13846

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47#13846
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 91300);