Finite Group Databasebeta

#365×Dic47 #26131664

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

Aliases

direct product#365×Dic47

Splittings

SylowC47 ⋊ C4×#365

Subgroups

subgroupG/H
centerC22#106×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#365C2
socleC22×C47C2×#106
prime radicalC23×C47C2×SD16
cosocleC22×C8×C47C23
hypercenterC2×#365D47
hypocenterC47C4×#365
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

330 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, 84954);