Finite Group Databasebeta

C2×#20241298 #26106659

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#20241298

Splittings

SylowC47 ⋊ C2×#1307

Subgroups

subgroupG/H
centerC23C47⋊#95
commutatorC23×C47C2×C42
FrattiniC2×C42C22×D47
FittingC2×C47×#432C2
socleC23×C47#95
prime radicalC24×C47C42
cosocleC2×C42×C47C23
hypercenterC2×#432D47
hypocenterC47C2×#1307
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

570 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59949);