C₇₃×#32801 #32942205

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₇₃×#32801

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

762 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 18688

A minimal faithful permutation representation — 4 generators on 105 points:

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

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, 25789);