Finite Group Databasebeta

#26147097

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C42

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #14639

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#400C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×#400D47
hypocenterC47#14639
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#400

1074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 100387);