Finite Group Databasebeta

D47×#2135 #26369118

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2135

Splittings

FittingC47×#2135 ⋊ C2
SylowC47 ⋊ C2×#2135

Subgroups

subgroupG/H
centerC2C2×#99×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×Q8C23×D47
FittingC47×#2135C2
socleC2×C47C22×#99
prime radicalC2×#41×D47C22
cosocleC2×Q8×C47C24
hypercenter#2135D47
hypocenterC47C2×#2135
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2135

1198 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

575 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322408);