C₅²×D₅₁ #14579359

order	2550
isoclinism	isoclinic class of D₅₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₅₁
unambiguous semidirect product	C₃⋊(C₅²×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅²×D₃)

	subgroup	G/H
center, hypercenter	C₅²	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅²

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)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2550, 22);