Finite Group Databasebeta

D29×#388 #16821920

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD29×#388

Splittings

FittingC29×#388 ⋊ C2
SylowC29 ⋊ C2×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#388C2
socle, cosocleC23×C29C24
prime radicalC24×D29C22
hypercenter#388D29
hypocenterC29C2×#388
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6938);