Finite Group Databasebeta

C2×#20245878 #26374668

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#20245878

Splittings

FittingC23×C42×C47 ⋊ C2
SylowC47 ⋊ C2×#2297

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC23×C42×C47C2
socleC24×C47C24
prime radicalC23×#10625350C2
cosocleC23×C47C25
hypercenterC23×C42D47
hypocenterC47C2×#2297
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C23×C42

6174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327958);