C₇×Dic₁₁ #64568

order	308
isoclinism	isoclinic class of D₁₁
automorphism	Aut(G) = C₂²×C₃×AGL(1,𝔽₁₁) (order 1320) · Inn(G) = D₁₁ · Out(G) = C₂²×C₃×C₅
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₄×C₇)

derived, Sylow	C₁₁ ⋊ C₄×C₇
Hall	C₇×C₁₁ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 308

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(308, 2);