C₁₇×#10613 #16868357

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

Aliases

direct product

C₁₇×#10613

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₂³×C₁₇	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 276 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) = 2176

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

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, 3601);