Finite Group Databasebeta

D47×#2222 #26370837

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD47×#2222

Splittings

FittingC47×#2222 ⋊ C2
SylowC47 ⋊ C2×#2222

Subgroups

subgroupG/H
centerC2#466×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2222C2
socleC2×C47C2×#466
prime radical#41×D47D4
hypercenter#2222D47
hypocenterC47C2×#2222
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #2222

638 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324127);