C₁₇×#13432 #16871176

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13432

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₇
prime radical	C₁₇×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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)(20,29)(21,24)(22,35)(23,28)(25,32)(26,33)(27,36)(30,43)(31,46)(34,41)(37,47)(38,48)(39,49)(40,45)(42,44);(19,24)(20,30)(21,33)(25,37)(26,28)(27,38)(29,42)(34,48)(35,41)(39,40)(43,46)(47,49);(18,20,21,31,23,30,33,44)(19,25,26,39,28,40,24,37)(22,32,34,47,36,45,48,49)(27,29,41,42,35,43,38,46)

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, 6420);