Finite Group Databasebeta

#431×Dic47 #26214405

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct product#431×Dic47

Splittings

SylowC47 ⋊ C4×#431

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC2×C47×#431C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×#431D47
hypocenterC47C4×#431
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C2×#431

1318 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167695);