Finite Group Databasebeta

D47×#1564 #26185248

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productD47×#1564

Splittings

FittingC47×#1564 ⋊ C2
SylowC47 ⋊ C2×#1564

Subgroups

subgroupG/H
centerC42D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC47×#1564C2
socleC22×C47C22×C4⋊C4
prime radicalC23×D47C4⋊C4
cosocleC42×C47C24
hypercenter#1564D47
hypocenterC47C2×#1564
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1564

830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138538);