C₃×C₇×AGL(1,𝔽₁₁) #14556336

order	2310
isoclinism	isoclinic class of AGL(1,𝔽₁₁)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₇×AGL(1,𝔽₁₁)
unambiguous semidirect product	D₁₁⋊(C₃×C₅×C₇)
unambiguous semidirect product	(C₁₁⋊C₅)⋊(C₂×C₃×C₇)
unambiguous semidirect product	(C₃×D₁₁)⋊(C₅×C₇)
unambiguous semidirect product	(C₃×C₇×D₁₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₃×C₇	AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁	C₂×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 231

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2310, 20);