Finite Group Databasebeta

#396×Dic47 #26138138

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#396×Dic47

Splittings

SylowC47 ⋊ C4×#396

Subgroups

subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#396C2
socle, cosocleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#396D47
hypocenterC47C4×#396
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

1966 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, 91428);