C₇₃×#13522 #32922926

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₃×#13522

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#2088
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
prime radical	C₂³×C₇₃	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ #405×C₇₃ ◁ G

240 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 105
transitive degree	μ_t(G) = 2336

A minimal faithful permutation representation — 3 generators on 105 points:

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

Conjugacy classes & character table

2482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6510);