D₇×D₁₃ #67246

order	364
isoclinism	isoclinic class of D₇×D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×D₁₃
unambiguous semidirect product	(C₁₃×D₇)⋊C₂
unambiguous semidirect product	(C₇×D₁₃)⋊C₂
unambiguous semidirect product	D₉₁⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃	C₂²
LCS	G ▷ C₇×C₁₃
UCS	C₁

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 91

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(364, 7);