C₇₁×#7477 #31828349

order	18176
nilpotency class	5
isoclinism	isoclinic class of #1418
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₁×#7477

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	#357
commutator	C₁₆	C₄²×C₇₁
Frattini, cosocle	C₂²×C₁₆	C₂²×C₇₁
prime radical	C₂³×C₇₁	D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ C₂²×C₈×C₇₁ ◁ C₂²×C₁₆×C₇₁ ◁ G

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

normal subgroups only

This group has 178 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) = 107
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 2 generators on 107 points:

(1,2,3,4)(5,6,9,15)(7,19,21,27)(8,24,26,16)(10,14,28,23)(11,22,29,36)(12,20,13,18)(17,32,34,25)(30,35,31,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(5,7,10,22,11,23,19,6,13,16,31,17,32,33,26,20,9,21,28,36,29,14,27,15,12,24,30,34,25,35,8,18)

Conjugacy classes & character table

3692 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 465);