C₇₁×#9931 #31830803

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₁×#9931

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇₁
prime radical	C₇₁×#3006	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂³×C₄×C₇₁ ◁ G

792 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 87
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 3 generators on 87 points:

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

Conjugacy classes & character table

2201 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 2919);