C₅×D₅₁ #92800

order	510
isoclinism	isoclinic class of D₅₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₅₁
unambiguous semidirect product	C₃⋊(C₅×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅×D₃)

	subgroup	G/H
center, hypercenter	C₅	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 255

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(510, 5);