Finite Group Databasebeta

D29×#421 #16828031

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD29×#421

Splittings

FittingC29×#421 ⋊ C2
SylowC29 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC29×#421C2
socleC2×C29C22×C22⋊C4
prime radicalC2×#41×D29C2
cosocleC2×C4×C29C24
hypercenter#421D29
hypocenterC29C2×#421
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 464

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, 13049);