Finite Group Databasebeta

#560×Dic47 #26378966

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

Aliases

direct product#560×Dic47

Splittings

SylowC47 ⋊ C4×#560

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
Fitting, prime radicalC2×C47×#560C2
socle, cosocleC23×C47C25
hypercenterC2×#560D47
hypocenterC47C4×#560
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#560

2568 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 332256);