C₇₃×#9862 #32919266

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₇₃×#9862

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₃	#127
commutator	C₄²	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
socle	C₂²×C₇₃	#390
prime radical	C₇₃×#3147	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

514 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 97
transitive degree	μ_t(G) = 9344

A minimal faithful permutation representation — 3 generators on 97 points:

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

Conjugacy classes & character table

3796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 2850);