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C11⋊AGL(1,𝔽19) #16836775

order3762
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊AGL(1,𝔽19)
unambiguous semidirect product#4296⋊D11

Splittings

Fitting, socle, derived, HallC11×C19 ⋊ C2×C9
HallC11×#4296 ⋊ C2
HallD209 ⋊ C9
Hall#4296 ⋊ D11
SylowC19 ⋊ C9×D11
SylowC11 ⋊ AGL(1,𝔽19)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C19C2×C9
prime radicalC11⋊(D19⋊C3)C3
cosocleC11×C19⋊C3C2×C3
LCSG ▷ C11×C19
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,3^2,11,19|b^3=c,d^a=d^10,e^a=e^18,e^b=e^4,e^c=e^7

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊AGL(1,𝔽19), C5×C11⋊AGL(1,𝔽19), C5⋊(C11⋊AGL(1,𝔽19)), …
maximal normal subgroup of(C11⋊C5)⋊AGL(1,𝔽19), C5×C11⋊AGL(1,𝔽19), C7×C11⋊AGL(1,𝔽19)
maximal quotient ofC5×C11⋊AGL(1,𝔽19), C5⋊(C11⋊AGL(1,𝔽19)), C7×C11⋊AGL(1,𝔽19), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 15);