Finite Group Databasebeta

C2×#20241531 #26136486

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241531

Splittings

FittingC2×C47×M64 ⋊ C2
SylowC47 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C16C22⋊D47
commutatorC4×C47C22×C16
FrattiniC2×C16C22×D47
FittingC2×C47×M64C2
socleC22×C47C22⋊C16
prime radicalC2×#10625350C8
cosocleC2×C16×C47C23
hypercenterC2×M64D47
hypocenterC47C2×#1401
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C2×M64

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 89776);