Finite Group Databasebeta

#26137638

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13790

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#389C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#389D47
hypocenterC47#13790
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

1522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90928);