Finite Group Databasebeta

#563×Dic47 #26378994

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

Aliases

direct product#563×Dic47

Splittings

SylowC47 ⋊ C4×#563

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×C47×#563C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterC2×#563D47
hypocenterC47C4×#563
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#563

2024 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, 332284);