Finite Group Databasebeta

#26137972

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

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13842

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1440C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenter#1440D47
hypocenterC47#13842
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1440

1814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 91262);