C₁₇×#7257 #16865001

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7257

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#327
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₂²×M₁₆	C₂²×C₁₇
socle	C₂×C₁₇	#1294
prime radical	C₂⁴×C₁₇	Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 302 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) = 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)(18,19,22,27,24,28,23,39)(20,29,31,44,33,48,32,47)(21,34,36,46,38,45,37,26)(25,40,41,49,43,35,42,30);(18,20,22,31,24,33,23,32)(19,25,27,41,28,43,39,42)(21,35,37,49,38,40,36,30)(26,44,45,29,46,47,34,48)

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, 245);