C₇₃×#13437 #32922841

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

Aliases

direct product

C₇₃×#13437

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇₃
prime radical	#535×C₇₃	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

422 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 86 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:

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

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6425);