C₂₉×C₅⋊D₅ #13089698

order	1450
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂₉×C₅⋊D₅
unambiguous semidirect product	C₅⋊(D₅×C₂₉)

Fitting, socle, Hall	C₅²×C₂₉ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₂₉

	subgroup	G/H
center, hypercenter	C₂₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₂₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂₉

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 725

A minimal faithful permutation representation — 3 generators on 39 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)(31,32)(33,34)(36,37)(38,39);(35,36,38,39,37);(30,31,33,34,32)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1450, 8);