C₅×D₅×C₁₃×C₁₉ #27134706

order	12350
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₅×C₁₃×C₁₉
unambiguous semidirect product	C₅⋊(C₂×C₅×C₁₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₁₃×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₅×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₅×C₁₃×C₁₉

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 2470

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5)(7,8)(9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42);(6,7,9,10,8)

4940 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12350, 17);