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D19×C11⋊C5 #14523458

order2090
isoclinismisoclinic class of D19×C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD19×C11⋊C5
unambiguous semidirect productC19⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D19)⋊C5

Splittings

Fitting, socle, derived, HallC11×C19 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C2
HallC11×D19 ⋊ C5
SylowC19 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C19C2×C5
LCSG ▷ C11×C19
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 209

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22,24,27,26)(23,25,29,30,28);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(20,21,23,26,22,24,28,30,25,27,29)

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×AGL(1,𝔽11), C2×D19×C11⋊C5, C7×D19×C11⋊C5, …
maximal normal subgroup ofD19×AGL(1,𝔽11), C2×D19×C11⋊C5, C7×D19×C11⋊C5, …
maximal quotient ofC11⋊C5×Dic19, C2×D19×C11⋊C5, C7×D19×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2090, 10);