Finite Group Databasebeta

C2×#20245399 #26370319

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245399

Splittings

SylowC47 ⋊ C2×#2201

Subgroups

subgroupG/H
centerC22#15689309
commutator, cosocleC2×D4×C47C24
FrattiniC2×D4C23×D47
FittingC2×C47×#458C2
socleC22×C47B(4,𝔽2)
prime radicalC2×H(5,𝔽2)×C47C22
hypercenterC2×#458D47
hypocenterC47C2×#2201
LCSG ▷ C2×D4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323609);