C₁₇×#12464 #16870208

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12464

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1675
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,25,31)(20,32,38,64)(21,39)(22,44,46,29)(23,28,33,59)(24,48,45,30)(26,49,53,35)(27,54)(34,67)(36,62,65,52)(37,51,72,63)(40,58)(41,75)(42,60)(43,55)(47,56)(50,69)(57,66)(61,76)(68,74)(70,78)(71,77)(73,80)(79,81);(18,20,33,65,24,37,22,35,25,38,23,36,45,72,46,49)(19,26,29,51,30,52,28,32,31,53,44,63,48,62,59,64)(21,34,66,81,41,69,40,68,43,71,47,73,42,70,54,76)(27,50,60,79,56,67,55,61,58,78,75,80,57,77,39,74);(18,21)(19,27)(20,34)(22,40)(23,47)(24,41)(25,43)(26,50)(28,55)(29,60)(30,56)(31,58)(32,61)(33,66)(35,68)(36,73)(37,69)(38,71)(39,59)(42,45)(44,75)(46,54)(48,57)(49,76)(51,79)(52,67)(53,78)(62,77)(63,80)(64,74)(65,81)(70,72)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5452);