Finite Group Databasebeta

#26142671

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42

Aliases

No aliases for this group.

Splittings

FittingC2×C47×#376 ⋊ C2
SylowC47 ⋊ #14260

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#376C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC2×#376D47
hypocenterC47#14260
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#376

1774 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,d^c=de,i^c=i^46

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 95961);