AGL(1,𝔽₁₁)×D₁₄₃ #44538168

order	31460
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	AGL(1,𝔽₁₁)×D₁₄₃
unambiguous semidirect product	D₁₁⋊(C₅×D₁₄₃)
unambiguous semidirect product	(C₁₁×AGL(1,𝔽₁₁))⋊D₁₃
unambiguous semidirect product	(C₁₃×AGL(1,𝔽₁₁))⋊D₁₁

Splittings

Fitting, socle, derived, Hall	C₁₁²×C₁₃ ⋊ C₂²×C₅
Hall	C₁₁×C₁₃×C₁₁⋊C₅ ⋊ C₂²
Hall	D₁₁×D₁₄₃ ⋊ C₅
Hall	C₁₁×C₁₁⋊C₅ ⋊ C₂×D₁₃
Sylow	C₁₁² ⋊ C₂×C₅×D₁₃
Sylow	C₁₃ ⋊ D₁₁×AGL(1,𝔽₁₁)

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₁₃	C₂²×C₅
LCS	G ▷ C₁₁²×C₁₃
UCS	C₁

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1430

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,7,3,9)(4,11,10,5,8)(13,14)(15,16)(17,18)(19,20)(21,22)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35);(2,3)(4,6)(5,8)(7,11)(9,10)(12,13,15,17,19,21,22,20,18,16,14)(23,24,26,28,30,32,34,35,33,31,29,27,25)

Conjugacy classes & character table

803 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 108);

AGL(1,𝔽11)×D143 #44538168