Finite Group Databasebeta

C22×(C2×D47)⋊C16 #26368942

order12032
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D47)⋊C16

Splittings

FittingC23×C16×C47 ⋊ C2
SylowC47 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D47
commutatorC2×C47C23×C16
FrattiniC2×C8C23×D47
FittingC23×C16×C47C2
socleC24×C47C2×C8
prime radicalC24×D47C8
cosocleC2×C8×C47C24
hypercenterC23×C16D47
hypocenterC47C22×C22⋊C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322232);