Finite Group Databasebeta

#504×Dic47 #26368921

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#504×Dic47

Splittings

SylowC47 ⋊ C4×#504

Subgroups

subgroupG/H
centerC2×C16C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC2×C47×#504C2
socleC22×C47C23×C8
prime radicalC2×#41×C47C2×C4
cosocleC2×C8×C47C24
hypercenterC2×#504D47
hypocenterC47C4×#504
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C16 ◁ C2×#504

834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322211);