Finite Group Databasebeta

C2×#358×D47 #26369152

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#358×D47

Splittings

FittingC2×C47×#358 ⋊ C2
SylowC47 ⋊ C22×#358

Subgroups

subgroupG/H
centerC23D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#358C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC2×C8×C47C24
hypercenterC2×#358D47
hypocenterC47C22×#358
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322442);