C₂×C₁₇×#2035 #16881220

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂⁵×C₁₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ C₂⁴×C₄×C₁₇ ◁ G

1662 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(8,9)(11,12,14,17)(13,15,18,16);(3,4)(5,6)(7,8)(9,10);(4,6)(7,9,10,8)(12,15)(13,18)(16,17)

1088 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 16464);