C₁₇×#13444 #16871188

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13444

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#2054
prime radical	C₁₇×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 392 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) = 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)(20,21)(22,35)(23,43)(24,45)(25,30)(26,31)(27,37)(28,42)(29,41)(32,47)(33,49)(34,39)(36,40)(38,46)(44,48);(18,20)(19,26)(21,35)(22,40)(23,27)(24,46)(25,34)(28,38)(29,36)(30,47)(31,42)(32,44)(33,41)(37,45)(39,43)(48,49);(18,21,22,36,41,49,44,47,25,39,23,37,24,38,42,26)(19,27,28,34,45,32,43,33,30,40,48,20,29,31,35,46)

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, 6432);