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D19×C31⋊C3 #16812969

order3534
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD19×C31⋊C3

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C2×C3
HallC19×C31⋊C3 ⋊ C2
HallC31×D19 ⋊ C3
SylowC31 ⋊ C3×D19
SylowC19 ⋊ C2×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C31C2×C3
LCSG ▷ C19×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 589

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22,24)(23,26,31)(25,29,28)(27,33,40)(30,36,38)(32,34,35)(37,43,47)(39,44,45)(41,48,42)(46,49,50);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(20,21,23,27,34,24,28,35,42,48,31,38,45,33,41,40,47,50,43,26,32,39,46,49,36,22,25,30,37,44,29)

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D19×C31⋊C3, C31⋊C3×D95, D19×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC5×D19×C31⋊C3, D19×(C31⋊C3)⋊C5, C7×D19×C31⋊C3
maximal quotient ofC5×D19×C31⋊C3, C31⋊C3×D95, C7×D19×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3534, 17);