C₂²×C₁₇×#525 #16920403

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂²×C₁₇×#525

	subgroup	G/H
center	C₂³×C₄×C₁₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
socle	C₂⁴×C₁₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₇ ◁ G

14334 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 6 generators on 33 points:

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

1904 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55647);