Finite Group Databasebeta

C2×#20245287 #26369720

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245287

Splittings

SylowC47 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#15689235
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
Fitting, prime radicalC2×C47×#509C2
socleC22×C47#442
cosocleC2×C8×C47C24
hypercenterC2×#509D47
hypocenterC47C2×AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

710 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323010);