Finite Group Databasebeta

C4×#15689087 #26213820

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#15689087

Splittings

SylowC47 ⋊ C4×#407

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC23×C42×C47C2
socleC23×C47C23×C4
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC23×C42D47
hypocenterC47C4×#407
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C23×C42

2246 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167110);