Finite Group Databasebeta

#367×Dic47 #26131683

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

Aliases

direct product#367×Dic47

Splittings

SylowC47 ⋊ C4×#367

Subgroups

subgroupG/H
centerC23D8×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#367C2
socle, prime radicalC23×C47C2×D8
cosocleC22×C8×C47C23
hypercenterC2×#367D47
hypocenterC47C4×#367
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

366 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84973);