C₇₃×#11913 #32921317

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₃×#11913

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#1530
commutator	C₄²	C₂²×C₄×C₇₃
Frattini, cosocle	#97	C₂³×C₇₃
prime radical	C₇₃×#3176	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ #405×C₇₃ ◁ G

296 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 94 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:

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

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, 4901);