Finite Group Databasebeta

D47×#1335 #26126059

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD47×#1335

Splittings

FittingC47×#1335 ⋊ C2
SylowC47 ⋊ C2×#1335

Subgroups

subgroupG/H
centerC8D8×D47
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC47×#1335C2
socleC2×C47C2×D4⋊C8
prime radical#135×D47C4
cosocleC4×C8×C47C23
hypercenter#1335D47
hypocenterC47C2×#1335
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ #1335

414 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, 79349);