Finite Group Databasebeta

← Prev (#11929416) Next (#11929418) →

C11⋊(D19⋊C3) #11929417

order1254
isoclinismisoclinic class of C11⋊(D19⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊D11
unambiguous semidirect productD209⋊C3

Splittings

Fitting, socle, derived, HallC11×C19 ⋊ C2×C3
HallC11×C19⋊C3 ⋊ C2
HallD209 ⋊ C3
HallC19⋊C3 ⋊ D11
SylowC19 ⋊ C3×D11
SylowC11 ⋊ D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C19C2×C3
LCSG ▷ C11×C19
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D19⋊C3, C2×C11⋊(D19⋊C3), C11⋊AGL(1,𝔽19), …
maximal normal subgroup ofD11×D19⋊C3, C2×C11⋊(D19⋊C3), C11⋊AGL(1,𝔽19), …
maximal quotient ofC11⋊((C19⋊C3)⋊C4), C2×C11⋊(D19⋊C3), C11⋊(#4294⋊C2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 3);