C₁₁×C₂₉×AGL(1,𝔽₇) #27211538

order	13398
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₂₉×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₁₁×C₂₉)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₁₁×C₂₉)
unambiguous semidirect product	(C₁₁×D₇)⋊(C₃×C₂₉)
unambiguous semidirect product	(D₇×C₂₉)⋊(C₃×C₁₁)
unambiguous semidirect product	(C₁₁×D₇×C₂₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₁×C₂₉	AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₂₉	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₁×C₂₉

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 2233

A minimal faithful permutation representation — 2 generators on 47 points:

(2,5,6,3,4,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47);(1,2,4,7,6,5,3)

2233 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13398, 29);