Finite Group Databasebeta

D29×#428 #16828073

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

Aliases

direct productD29×#428

Splittings

FittingC29×#428 ⋊ C2
SylowC29 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
FittingC29×#428C2
socleC22×C29C22×D4
prime radicalC23×D29D4
cosocleC2×C4×C29C24
hypercenter#428D29
hypocenterC29C2×#428
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

536 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, 13091);