Finite Group Databasebeta

#352×Dic47 #26131417

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#352×Dic47

Splittings

SylowC47 ⋊ C4×#352

Subgroups

subgroupG/H
centerC22#99×D47
commutatorC23×C47C2×C42
FrattiniC22×D4C22×D47
FittingC2×C47×#352C2
socleC22×C47C2×#99
prime radical, cosocleC22×D4×C47C23
hypercenterC2×#352D47
hypocenterC47C4×#352
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84707);