D₅×#4296 #13133754

order	1710
isoclinism	isoclinic class of D₅×#4296
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×#4296
unambiguous semidirect product	C₅⋊(C₂×#4296)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉	C₂×C₉
prime radical	D₅×C₁₉⋊C₃	C₃
cosocle	C₅×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1710, 14);