C₁₇×C₅²⋊C₃ #11929708

order	1275
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₇ · Schur multiplier (H₂) = C₅

Aliases

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

Fitting, socle, Hall	C₅²×C₁₇ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₁₇

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

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 255

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21)(20,24,26)(22,27,30)(23,29,32)(25,28,31);(18,20,25,30,32)(19,24,28,22,23)(21,27,26,29,31)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1275, 2);