Finite Group Databasebeta

D47×#1764 #26214104

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productD47×#1764

Splittings

FittingC47×#1764 ⋊ C2
SylowC47 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1764C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1764D47
hypocenterC47C2×#1764
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1764

1558 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, 167394);