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C5×AGL(1,𝔽19) #13133753

order1710
isoclinismisoclinic class of AGL(1,𝔽19)
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C2×C5×C9
HallC5×#4296 ⋊ C2
HallC5×D19 ⋊ C9
Hall#4296 ⋊ C2×C5
HallD19 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC5AGL(1,𝔽19)
commutator, hypocenterC19C2×C5×C9
FrattiniC1G
Fitting, socleC5×C19C2×C9
prime radicalC5×D19⋊C3C3
cosocleC19⋊C3C2×C3×C5
LCSG ▷ C19
UCSC1 ◁ C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 95

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽19), C2×C5×AGL(1,𝔽19), C5×C7×AGL(1,𝔽19), …
maximal normal subgroup ofD5×AGL(1,𝔽19), C2×C5×AGL(1,𝔽19), C5×C7×AGL(1,𝔽19), …
maximal quotient ofC5×#4296⋊C4, C2×C5×AGL(1,𝔽19), C5×C7×AGL(1,𝔽19), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1710, 13);