C₇₃×#13707 #32923111

order	18688
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₃×#13707

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₃
prime radical	C₂×D₁₆×C₇₃	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄²×C₇₃ ◁ C₄×C₈×C₇₃ ◁ C₄×C₁₆×C₇₃ ◁ G

170 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 113
transitive degree	μ_t(G) = 9344

A minimal faithful permutation representation — 3 generators on 113 points:

(1,2,4,6)(3,7,8,5)(9,10,11,15)(12,16,20,28)(13,26,21,38)(14,27,22,19)(17,33,29,23)(18,35,30,24)(25,36,37,32)(31,40,34,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(1,3,4,8)(2,5,6,7)(10,15)(16,28)(17,29)(18,30)(19,27)(26,38)(31,34)(32,36);(10,16)(12,23)(13,24)(14,22)(15,28)(17,18)(19,36)(20,33)(21,35)(25,40)(26,31)(27,32)(29,30)(34,38)(37,39)

Conjugacy classes & character table

3577 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6695);