Finite Group Databasebeta

C4×#15689080 #26213619

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

Aliases

direct productC4×#15689080

Splittings

FittingC4×#97×C47 ⋊ C2
SylowC47 ⋊ C4×#405

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C2×C43
FrattiniC22×C4C23×D47
FittingC4×#97×C47C2
socleC23×C47C23×C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenterC4×#97D47
hypocenterC47C4×#405
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C4×#97

1526 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, 166909);