Finite Group Databasebeta

D47×#2197 #26370282

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2197

Splittings

FittingC47×#2197 ⋊ C2
SylowC47 ⋊ C2×#2197

Subgroups

subgroupG/H
centerC2B(4,𝔽2)×D47
commutator, cosocleC2×D4×C47C24
FrattiniC2×D4C23×D47
FittingC47×#2197C2
socleC2×C47C2×B(4,𝔽2)
prime radicalB(4,𝔽2)×D47C2
hypercenter#2197D47
hypocenterC47C2×#2197
LCSG ▷ C2×D4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #2197

1320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

500 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323572);