Finite Group Databasebeta

C2×#20246209 #26375451

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#20246209

Splittings

FittingC2×C47×#390 ⋊ C2
SylowC47 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#390C2
socleC24×C47C24
prime radicalC23×D4×D47C2
cosocleC23×C47C25
hypercenterC2×#390D47
hypocenterC47C2×D4×C22⋊C4
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

8774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328741);