Finite Group Databasebeta

C2×#20245284 #26369717

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

Aliases

direct productC2×#20245284

Splittings

FittingC2×C47×#442 ⋊ C2
SylowC47 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#15689233
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#442C2
socleC22×C47#442
prime radicalC2×#15689559C2
cosocleC2×C8×C47C24
hypercenterC2×#442D47
hypocenterC47C2×AGL(1,ℤ/16)
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#442

710 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323007);