Finite Group Databasebeta

D29×#475 #16829253

order3712
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productD29×#475

Splittings

FittingC29×#475 ⋊ C2
SylowC29 ⋊ C2×#475

Subgroups

subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#475C2
socleC22×C29C22×D4
prime radicalC22×D29C2×D4
hypercenter#475D29
hypocenterC29C2×#475
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #475

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 14271);