Finite Group Databasebeta

#26244423

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

Aliases

No aliases for this group.

Splittings

FittingC2×C47×#532 ⋊ C2
SylowC47 ⋊ #23567

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#532C2
socleC23×C47C22×D4
hypercenterC2×#532D47
hypocenterC47#23567
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#532

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197713);