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C5×C7×AGL(1,𝔽19) #26046121

order11970
isoclinismisoclinic class of AGL(1,𝔽19)
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C2×C5×C7)

Splittings

Fitting, socle, HallC5×C7×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C2×C5×C7×C9
HallC5×C7×#4296 ⋊ C2
HallC5×C7×D19 ⋊ C9
HallC7×#4296 ⋊ C2×C5
HallC5×#4296 ⋊ C2×C7
HallC7×D19 ⋊ C5×C9
HallC5×D19 ⋊ C7×C9
Hall#4296 ⋊ C2×C5×C7
HallC7×C19 ⋊ C2×C5×C9
HallC5×C19 ⋊ C2×C7×C9
HallD19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7AGL(1,𝔽19)
commutator, hypocenterC19C2×C5×C7×C9
FrattiniC1G
Fitting, socleC5×C7×C19C2×C9
prime radicalC5×C7×D19⋊C3C3
cosocleC19⋊C3C2×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D7×AGL(1,𝔽19), C7×D5×AGL(1,𝔽19), D35×AGL(1,𝔽19), …
maximal normal subgroup ofC5×D7×AGL(1,𝔽19), C7×D5×AGL(1,𝔽19), D35×AGL(1,𝔽19), …
maximal quotient ofC5×C7×#4296⋊C4, C2×C5×C7×AGL(1,𝔽19)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 50);