Finite Group Databasebeta

C2×#20241241 #26105990

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#20241241

Splittings

SylowC47 ⋊ C2×#1284

Subgroups

subgroupG/H
centerC23C47⋊#95
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C4×C22⋊C4×C47C2
socleC23×C47#95
prime radicalC25×C47D4
cosocleC23×C4×C47C23
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#1284
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1118 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, 59280);