C₁₇×#10611 #16868355

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10611

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂×C₁₇×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 1088

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)(18,19,21,27,23,25,22,26)(20,28,29,24,31,32,30,33)(34,35)(36,44)(37,42)(38,41)(39,43)(40,46)(45,48)(47,49);(18,20,21,29,23,31,22,30)(19,24,26,28,25,33,27,32)(34,36,37,46,39,45,38,47)(35,40,41,44,43,49,42,48);(19,25)(20,29)(21,22)(24,32)(28,33)(30,31)(35,41)(36,45)(37,38)(40,44)(42,43)(48,49)

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, 3599);