Finite Group Databasebeta

#492×Dic47 #26224700

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#492×Dic47

Splittings

SylowC47 ⋊ C4×#492

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#492C2
socleC23×C47C22×D4
prime radicalC2×#127×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#492D47
hypocenterC47C4×#492
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

1254 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, 177990);