C₁₇×#7449 #16865193

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×#7449

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
prime radical	C₂²×C₁₇	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 126 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)(18,19,22,28,45,31,47,57,25,32,46,30,24,48,23,29)(20,33,35,64,49,66,73,81,38,67,72,56,37,74,36,65)(21,39,41,27,55,58,68,60,44,76,79,61,43,59,42,75)(26,40,50,34,53,69,62,80,54,78,52,71,63,77,51,70);(18,20,25,38)(19,26,32,54)(21,40,44,78)(22,36,46,73)(23,35,47,72)(24,49,45,37)(27,56,61,64)(28,51,30,62)(29,50,57,52)(31,63,48,53)(33,58,67,59)(34,68,71,42)(39,74,76,66)(41,70,79,80)(43,69,55,77)(60,81,75,65)

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, 437);