C₅×D₉×C₂₉ #14579707

order	2610
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₉×C₂₉
unambiguous semidirect product	C₉⋊(C₂×C₅×C₂₉)

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₂₉
Frattini	C₃	C₅×D₃×C₂₉
Fitting	C₅×C₉×C₂₉	C₂
socle	C₃×C₅×C₂₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₂₉

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1305

A minimal faithful permutation representation — 2 generators on 43 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2610, 5);