D₅×C₁₉×D₃₅ #27210915

order	13300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×C₁₉×D₃₅
unambiguous semidirect product	(C₅×D₅)⋊(D₇×C₁₉)
unambiguous semidirect product	(C₇×D₅)⋊(D₅×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₅×D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₉

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1330

A minimal faithful permutation representation — 2 generators on 36 points:

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

1444 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 73);