Finite Group Databasebeta

C4×M16×Dic47 #26213608

order12032
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×M16×Dic47

Splittings

SylowC47 ⋊ C42×M16

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C2×C43
FrattiniC22×C4C23×D47
FittingC2×C4×M16×C47C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C42×M16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

1734 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, 166898);