Finite Group Databasebeta

C2×#20242311 #26188354

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

Aliases

direct productC2×#20242311

Splittings

FittingC2×C47×#543 ⋊ C2
SylowC47 ⋊ C2×#1596

Subgroups

subgroupG/H
centerC23#13093993
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#543C2
socleC23×C47#120
prime radicalC2×#15689032C2
hypercenterC2×#543D47
hypocenterC47C2×#1596
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#543

1696 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, 141644);