Finite Group Databasebeta

#556×Dic47 #26376235

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

Aliases

direct product#556×Dic47

Splittings

SylowC47 ⋊ C4×#556

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC2×C47×#556C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterC2×#556D47
hypocenterC47C4×#556
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

2340 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329525);