C₁₉×D₁₃ #92458

order	494
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₁₃
unambiguous semidirect product	C₁₃⋊(C₂×C₁₉)

Fitting, socle, Hall	C₁₃×C₁₉ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₉

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 247

A minimal faithful permutation representation — 2 generators on 32 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(1,2,4,6,8,10,12,13,11,9,7,5,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(494, 1);