C₅²×D₃×C₁₇ #14579358

order	2550
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₁₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃×C₁₇
unambiguous semidirect product	C₃⋊(C₂×C₅²×C₁₇)

	subgroup	G/H
center, hypercenter	C₅²×C₁₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅²×C₁₇

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1275

A minimal faithful permutation representation — 2 generators on 30 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);(6,7,8,9,10)(12,13)

1275 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2550, 21);