Finite Group Databasebeta

#26137594

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

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13786

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC22×C4×Q8×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47#13786
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×Q8

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|a^2=g,b^2=h,c^2=efg,d^2=e,b^a=be,c^a=cf,d^a=de,i^a=i^46,c^b=ce,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, 90884);