Finite Group Databasebeta

D47×#1797 #26215628

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productD47×#1797

Splittings

FittingC47×#1797 ⋊ C2
SylowC47 ⋊ C2×#1797

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC47×#1797C2
socleC23×C47C23×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1797D47
hypocenterC47C2×#1797
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1797

2222 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, 168918);