Finite Group Databasebeta

D47×#1375 #26131123

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD47×#1375

Splittings

FittingC47×#1375 ⋊ C2
SylowC47 ⋊ C2×#1375

Subgroups

subgroupG/H
centerC2×C4C42×D47
commutatorC4×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC47×#1375C2
socleC22×C47C2×#97
prime radicalC23×D47M16
cosocleC22×C8×C47C23
hypercenter#1375D47
hypocenterC47C2×#1375
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #1375

630 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, 84413);