Finite Group Databasebeta

D47×#1974 #26220215

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

Aliases

direct productD47×#1974

Splittings

FittingC47×#1974 ⋊ C2
SylowC47 ⋊ C2×#1974

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1974C2
socleC22×C47C2×C4×D4
prime radicalC2×#135×D47C2
cosocleC22×C4×C47C24
hypercenter#1974D47
hypocenterC47C2×#1974
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

1558 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, 173505);