C₇₃×#13439 #32922843

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₃×#13439

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
prime radical	C₂²×D₁₆×C₇₃	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ #405×C₇₃ ◁ G

418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 109
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 3 generators on 109 points:

(1,2)(3,4)(5,6)(7,18)(8,12)(9,24)(10,27)(11,17)(13,19)(14,22)(15,25)(16,23)(20,35)(21,31)(26,30)(28,33)(29,36)(32,34)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(6,12)(7,19)(8,22)(9,25)(10,23)(14,16)(15,27)(17,24)(18,28)(20,36)(21,26)(29,32)(31,35)(33,34);(2,4)(5,7,8,19,23,33,25,36,11,21,9,26,10,20,22,34)(6,13,14,18,27,32,24,35,17,30,15,31,16,29,12,28)

Conjugacy classes & character table

2920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6427);