Finite Group Databasebeta

C4×#15689813 #26376174

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

Aliases

direct productC4×#15689813

Splittings

SylowC47 ⋊ C4×#552

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC42×D4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterC42×D4D47
hypocenterC47C4×#552
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C42×D4

2376 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 329464);