C₁₇×#7226 #16864970

order	4352
nilpotency class	3
isoclinism	isoclinic class of #7225
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7226

Subgroups

	subgroup	G/H
center	C₄×C₁₇	H(3,ℤ/4)
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₄×M₁₆	C₂²×C₁₇
socle	C₂×C₁₇	#1288
prime radical	C₂³×C₁₇	#104
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ G

180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 544

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,30,41)(21,32,33,46)(22,26)(23,27)(24,29)(25,34,39,47)(31,42,45,49)(35,38)(36,43)(37,44)(40,48);(18,20)(19,24,26,36,27,37,38,40)(21,29)(22,31)(23,30)(25,28,32,42,39,41,46,49)(33,44)(34,43)(35,45)(47,48)

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, 214);