D₇×D₁₁ #64571

order	308
isoclinism	isoclinic class of D₇×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×D₁₁
unambiguous semidirect product	(C₁₁×D₇)⋊C₂
unambiguous semidirect product	(C₇×D₁₁)⋊C₂
unambiguous semidirect product	D₇₇⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁	C₂²
LCS	G ▷ C₇×C₁₁
UCS	C₁

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 77

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(308, 5);