C₁₇×#7447 #16865191

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7447
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7447

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

130 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 81 points:

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

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, 435);