C₂×C₅×C₇×D₅×C₁₉ #27210929

order	13300
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×C₇×D₅×C₁₉
unambiguous semidirect product	C₅⋊(C₂²×C₅×C₇×C₁₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₅×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₇×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₇×C₁₉

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 2660

A minimal faithful permutation representation — 2 generators on 38 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);(6,7,9,10,8)(37,38)

5320 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 87);