Finite Group Databasebeta

#529×Dic47 #26374785

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#529×Dic47

Splittings

SylowC47 ⋊ C4×#529

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#529C2
socle, cosocleC23×C47C25
prime radicalC2×#121×C47C22
hypercenterC2×#529D47
hypocenterC47C4×#529
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#529

2670 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328075);