Finite Group Databasebeta

C2×SD32×Dic47 #26369546

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×SD32×Dic47

Splittings

SylowC47 ⋊ C2×C4×SD32

Subgroups

subgroupG/H
centerC23D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC22×SD32×C47C2
socleC23×C47C2×D8
prime radicalC22×D8×C47C22
cosocleC2×C8×C47C24
hypercenterC22×SD32D47
hypocenterC47C2×C4×SD32
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

742 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, 322836);