Finite Group Databasebeta

#542×Dic47 #26375407

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

Aliases

direct product#542×Dic47

Splittings

SylowC47 ⋊ C4×#542

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×C47×#542C2
socle, cosocleC23×C47C25
prime radicalC2×#121×C47C22
hypercenterC2×#542D47
hypocenterC47C4×#542
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#542

2294 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, 328697);