Finite Group Databasebeta

D47×#1788 #26215465

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD47×#1788

Splittings

FittingC47×#1788 ⋊ C2
SylowC47 ⋊ C2×#1788

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1788C2
socleC23×C47C22×D4
prime radicalC22×#41×D47C2
cosocleC22×C4×C47C24
hypercenter#1788D47
hypocenterC47C2×#1788
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

4070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168755);