Finite Group Databasebeta

C2×#20244665 #26244113

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

Aliases

direct productC2×#20244665

Splittings

SylowC47 ⋊ C2×#2049

Subgroups

subgroupG/H
centerC22#15689037
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#137×C47C2
socleC22×C47#394
prime radicalC22×#41×C47C22
hypercenterC22×#137D47
hypocenterC47C2×#2049
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

1322 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, 197403);