D₇×ΓL(1,𝔽₈)⋊AGL(1,𝔽₁₁) #44568550

order	32340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×ΓL(1,𝔽₈)⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(D₇×ΓL(1,𝔽₈))⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(D₇×C₁₁⋊AGL(1,𝔽₇))⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₁	C₂²×C₃×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁

168 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 462

A minimal faithful permutation representation — 2 generators on 25 points:

(2,6,7,5,10,3,4,11,8,9)(12,13,15,17,18,16,14)(20,23,24,21,22,25);(1,2,5,10,4,7,11,6,9,8,3)(13,14)(15,16)(17,18)(19,20,22,25,24,23,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 252);