Finite Group Databasebeta

← Prev (#15693255) Next (#15693257) →

C19⋊C3×D29 #15693256

order3306
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC19⋊C3×D29
unambiguous semidirect productC29⋊(C2×C19⋊C3)
unambiguous semidirect product(C19×D29)⋊C3

Splittings

Fitting, socle, derived, HallC19×C29 ⋊ C2×C3
HallC29×C19⋊C3 ⋊ C2
HallC19×D29 ⋊ C3
SylowC29 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C29C2×C3
LCSG ▷ C19×C29
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 551

A minimal faithful permutation representation — 2 generators on 48 points:

(2,3,5)(4,7,8)(6,10,9)(11,15,13)(12,16,14)(17,19,18)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(1,2,4,8,13,18,15,3,6,11,16,5,9,14,7,12,17,19,10)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C19⋊C3×D29, C19⋊C3×D145, C7×C19⋊C3×D29, …
maximal normal subgroup ofC5×C19⋊C3×D29, C7×C19⋊C3×D29, C19⋊C3×D29⋊C7, …
maximal quotient ofC5×C19⋊C3×D29, C19⋊C3×D145, C7×C19⋊C3×D29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3306, 10);