C₁₇×#11994 #16869738

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11994
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11994

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1558
commutator	C₄²	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 258 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4982);