C₇₃×#11868 #32921272

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

Aliases

direct product

C₇₃×#11868

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#1519
commutator	C₂×C₈	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₇₃
prime radical	C₇₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#131×C₇₃ ◁ G

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

normal subgroups only

This group has 396 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) = 105
transitive degree	μ_t(G) = 2336

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

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

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, 4856);