C₁₇×#10664 #16868408

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#10664

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
socle	C₂²×C₁₇	#399
prime radical	C₂³×C₁₇	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

304 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 106 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)(18,19,22,26,23,27,21,25)(20,28,29,33,30,32,31,24)(34,35,37,41,38,42,46,39)(36,43,44,48,45,49,47,40);(18,20,21,29,23,30,22,31)(19,24,25,28,27,33,26,32)(35,39)(37,46)(40,43)(41,42)(44,47)(48,49);(18,21,23,22)(19,25,27,26)(20,29,30,31)(24,32,33,28)(34,36,38,45)(35,40,42,48)(37,47,46,44)(39,43,41,49)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3652);