C₁₇×#12730 #16870474

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12727
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#12730

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1782
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₇
prime radical	C₂×#41×C₁₇	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₁₇×#519 ◁ G

666 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 138 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)(18,19,23,28,24,29,20,30)(21,33,36,44,35,26,31,42)(22,27,32,40,38,43,37,25)(34,47,45,39,49,41,48,46);(18,20,24,23)(19,25,29,40)(21,31,35,36)(22,37,38,32)(26,39,33,46)(27,28,43,30)(34,48,49,45)(41,42,47,44);(18,21,24,35)(19,26)(20,31,23,36)(22,34,38,49)(25,39)(27,41)(28,42)(29,33)(30,44)(32,45,37,48)(40,46)(43,47)

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, 5718);