C₁₇×#7218 #16864962

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7217
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7218

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	#102
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 202 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) = 1088

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)(36,46,48,60)(37,43)(38,53)(39,55)(40,45)(41,47,56,61)(42,51)(44,54)(49,64,62,58)(50,65,63,57)(52,59);(18,20)(19,23,25,30)(21,27)(22,28)(24,26,31,32)(29,33)(34,36,38,49,54,63,52,61,40,48,51,62,39,50,37,47)(35,41,43,57,55,64,42,46,45,56,59,65,44,58,53,60)

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, 206);