C₇₃×#13373 #32922777

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

Aliases

direct product

C₇₃×#13373

Subgroups

	subgroup	G/H
center	C₄×C₇₃	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
socle	C₂×C₇₃	#2023
prime radical	C₂×#135×C₇₃	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#97×C₇₃ ◁ G

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

normal subgroups only

This group has 364 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)(3,12,14,29)(4,17)(5,10)(6,22)(7,11)(8,15,24,31)(9,21)(13,30,16,26)(18,28)(19,27,32,23)(20,25)(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);(3,13,14,16)(4,18)(8,23,24,27)(9,25)(12,26,29,30)(15,32,31,19)(17,28)(20,21);(1,3)(2,8)(4,19)(5,16)(6,13)(7,14)(9,26)(10,27)(11,24)(12,28)(15,20)(17,29)(18,32)(21,31)(22,23)(25,30)

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, 6361);