Finite Group Databasebeta

#26216151

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #20714

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1779C2
socleC23×C47C23×C4
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenter#1779D47
hypocenterC47#20714
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1779

2038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 169441);