C₇₁×#11911 #31832783

order	18176
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₁×#11911

Subgroups

	subgroup	G/H
center	C₄×C₇₁	#329
commutator	C₄²	C₂²×C₄×C₇₁
Frattini, cosocle	#97	C₂³×C₇₁
socle	C₂×C₇₁	C₂×#329
prime radical	#532×C₇₁	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ C₂×#97×C₇₁ ◁ G

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

normal subgroups only

This group has 318 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) = 2272

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

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

Conjugacy classes & character table

2840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 4899);