C₁₇×#7220 #16864964

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7217
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7220

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#340
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₇
prime radical	C₂³×C₁₇	#103
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 65
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,32)(21,24)(22,25)(23,27,30,33)(29,31)(34,35,38,44,41,46,40,56)(36,47,49,62,51,63,54,58)(37,45,39,55,53,61,52,43)(42,50,57,48,60,64,59,65);(18,20)(19,23,25,30)(21,27)(22,28)(24,26,31,32)(29,33)(34,36,39,50,38,54,53,65,41,51,52,64,40,49,37,48)(35,42,45,58,56,57,43,47,46,60,61,62,44,59,55,63)

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, 208);