Finite Group Databasebeta

D29×#440 #16828267

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

Aliases

direct productD29×#440

Splittings

FittingC29×#440 ⋊ C2
SylowC29 ⋊ C2×#440

Subgroups

subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC29×#440C2
socleC22×C29C22×D4
prime radicalC2×D4×D29C22
cosocleC2×C4×C29C24
hypercenter#440D29
hypocenterC29C2×#440
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #440

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13285);