C₇₃×#9995 #32919399

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

Aliases

direct product

C₇₃×#9995

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₂⁴×C₇₃	#41
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

510 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 4672

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

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

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, 2983);