C₇₃×#10393 #32919797

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₃×#10393

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₇₃
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂⁵×C₇₃ ◁ G

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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:

(1,2,5,9)(3,7,14,23)(4,15)(6,11,19,10)(8,17)(12,27)(13,22,29,21)(16,24)(18,25)(20,30)(26,31)(28,32)(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)(2,7)(4,16,17,12)(5,14)(6,13)(8,24,15,27)(9,23)(10,21)(11,22)(18,30,31,28)(19,29)(20,25,32,26);(1,4,6,18)(2,8,11,26)(3,12,13,28)(5,17,19,31)(7,20,22,24)(9,15,10,25)(14,16,29,30)(21,27,23,32)

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 3381);