C₁₇×#7371 #16865115

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

Aliases

direct product

C₁₇×#7371

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#353
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	#384	C₂²×C₁₇
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#384 ◁ G

190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 359);