Finite Group Databasebeta

#26138798

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4

Aliases

No aliases for this group.

Splittings

SylowC47 ⋊ #13937

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
Fitting, prime radicalC23×#41×C47C2
socle, cosocleC24×C47C24
hypercenterC23×#41D47
hypocenterC47#13937
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×#41

4470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 92088);