Finite Group Databasebeta

C2×#20244468 #26243323

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20244468

Splittings

FittingC2×C47×#336 ⋊ C2
SylowC47 ⋊ C2×#2012

Subgroups

subgroupG/H
centerC24C2×D188
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#336C2
socleC24×C47C2×D4
prime radicalC23×D376C2
hypercenterC2×#336D47
hypocenterC47C2×#2012
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

2382 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196613);