Finite Group Databasebeta

#509×Dic47 #26369598

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#509×Dic47

Splittings

SylowC47 ⋊ C4×#509

Subgroups

subgroupG/H
centerC22C2×D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
Fitting, prime radicalC2×C47×#509C2
socleC22×C47C22×D8
cosocleC2×C8×C47C24
hypercenterC2×#509D47
hypocenterC47C4×#509
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

738 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322888);