C₁₇×#9070 #16866814

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#9070

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#120
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#386
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23,26,29)(20,27,28,30)(34,35,38,42,39,37,46,41)(36,40,44,48,45,43,49,47);(18,19,24,23,22,26,21,29)(20,25,27,31,28,33,30,32)(34,36,38,44,39,45,46,49)(35,40,42,48,37,43,41,47);(18,20,22,28)(19,25,26,33)(21,30,24,27)(23,31,29,32)(34,37)(35,39)(36,43)(38,41)(40,45)(42,46)(44,47)(48,49)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 2058);