C₁₇×#13717 #16871461

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13717
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#13717

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2233
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
prime radical	C₁₇×#2218	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ C₂×C₁₇×M₃₂ ◁ G

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

normal subgroups only

This group has 170 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 — 3 generators on 49 points:

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6705);