C₁₇×#7374 #16865118

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7374

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#353
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#423	C₂²×C₁₇
socle	C₂×C₁₇	#1325
prime radical	C₂³×C₁₇	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#423 ◁ G

148 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 544

A minimal faithful permutation representation — 2 generators on 49 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 362);