Finite Group Databasebeta

D47×#1813 #26215926

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#1813

Splittings

FittingC47×#1813 ⋊ C2
SylowC47 ⋊ C2×#1813

Subgroups

subgroupG/H
centerC4#117×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1813C2
socleC2×C47C2×#380
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1813D47
hypocenterC47C2×#1813
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1813

1314 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 169216);