D₉×D₁₃ #90836

order	468
isoclinism	isoclinic class of D₉×D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉×D₁₃
unambiguous semidirect product	(C₁₃×D₉)⋊C₂
unambiguous semidirect product	(C₉×D₁₃)⋊C₂
unambiguous semidirect product	D₁₁₇⋊C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃	C₂²
Frattini	C₃	D₃×D₁₃
socle	C₃×C₁₃	C₂×D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 117

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 11);