C₅×C₃⋊D₅₁ #13095264

order	1530
isoclinism	isoclinic class of C₃⋊D₅₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₃⋊D₅₁
unambiguous semidirect product	C₃⋊(C₅×D₅₁)
unambiguous semidirect product	C₁₇⋊(C₅×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₅

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 765

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(24,25)(27,28);(6,7,9,11,13,15,17,19,21,22,20,18,16,14,12,10,8)(26,27,28);(23,24,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1530, 17);