C₂×C₁₇×#1706 #16877337

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₇	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

1046 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);(4,7)(5,8)(9,10)(12,15)(13,17)(16,18);(3,4,8,10,6,9,5,7);(11,12,13,15,14,16,17,18)

1292 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 12581);