Finite Group Databasebeta

#26249513

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

FittingC2×C47×#386 ⋊ C2
SylowC47 ⋊ #24056

Subgroups

subgroupG/H
centerC22C2×#13093992
commutator, cosocleC24×C47C24
FrattiniC24C23×D47
FittingC2×C47×#386C2
socleC22×C47C2×#120
prime radical#20257023C2
hypercenterC2×#386D47
hypocenterC47#24056
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C2×#386

1820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,47|c^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^46,c^b=cg,f^b=fh

Conjugacy classes & character table

1334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 202803);