C₇₃×#9466 #32918870

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₇₃×#9466

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₇₃
Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

726 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 4672

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

(1,2)(3,5,7,8)(4,6)(9,10,15,18,14,11,13,17)(12,16,22,24,21,19,20,23)(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);(1,3,4,7)(2,5)(6,8)(9,11,14,10)(12,19,21,16)(13,17,15,18)(20,23,22,24);(9,12,14,21)(10,16,11,19)(13,22,15,20)(17,24,18,23)

Conjugacy classes & character table

2701 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 2454);