C₅²×D₃×C₃₁ #17987883

order	4650
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₃₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃×C₃₁
unambiguous semidirect product	C₃⋊(C₂×C₅²×C₃₁)

	subgroup	G/H
center, hypercenter	C₅²×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅²×C₃₁

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 2325

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(6,7,8,9,10)(12,13)

2325 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4650, 53);