Finite Group Databasebeta

D47×#1312 #26125263

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productD47×#1312

Splittings

FittingC47×#1312 ⋊ C2
SylowC47 ⋊ C2×#1312

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D47
commutatorC2×C47C2×C4×C16
FittingC47×#1312C2
socleC22×C47C2×C4×C8
prime radicalC22×D47C4×C8
cosocleC4×C8×C47C23
hypercenter#1312D47
hypocenterC47C2×#1312
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ #1312

350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 78553);