Finite Group Databasebeta

C2×#357×D47 #26369148

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#357×D47

Splittings

FittingC2×C47×#357 ⋊ C2
SylowC47 ⋊ C22×#357

Subgroups

subgroupG/H
centerC23D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×D8×D47C2
cosocleC2×C8×C47C24
hypercenterC2×#357D47
hypocenterC47C22×#357
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

1470 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, 322438);