C₇₃×#11523 #32920927

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

Aliases

direct product

C₇₃×#11523

Subgroups

	subgroup	G/H
center	C₄×C₇₃	#410
commutator	C₂²×C₄	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₇₃
socle	C₂×C₇₃	#1464
prime radical	C₂×#41×C₇₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₄²×C₇₃ ◁ C₄×M₁₆×C₇₃ ◁ G

280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 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:

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

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, 4511);