C₇₁×#10361 #31831233

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₁×#10361

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 103
transitive degree	μ_t(G) = 18176

A minimal faithful permutation representation — 3 generators on 103 points:

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

Conjugacy classes & character table

2414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 3349);