Finite Group Databasebeta

C2×#20241513 #26131245

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20241513

Splittings

SylowC47 ⋊ C2×#1393

Subgroups

subgroupG/H
centerC23#13093939
commutatorC2×C4×C47C2×C42
FrattiniC22×D4C22×D47
FittingC2×C47×#390C2
socleC23×C47#99
prime radicalC23×D4×C47C22
cosocleC22×D4×C47C23
hypercenterC2×#390D47
hypocenterC47C2×#1393
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C2×#390

1154 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, 84535);