C₁₇×#10614 #16868358

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

Aliases

direct product

C₁₇×#10614

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

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, 3602);