Finite Group Databasebeta

C42×#10625350 #26374479

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC42×#10625350

Splittings

FittingC2×C43×C47 ⋊ C2
SylowC47 ⋊ C42×#41

Subgroups

subgroupG/H
centerC43C2×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C43×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#10625350C22
hypercenterC2×C43D47
hypocenterC47C42×#41
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C43 ◁ C2×C43

4086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327769);