Finite Group Databasebeta

#328×Dic47 #26107159

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

Aliases

direct product#328×Dic47

Splittings

SylowC47 ⋊ C4×#328

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#328C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#328D47
hypocenterC47C4×#328
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

732 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60449);