C₇₁×#7289 #31828161

order	18176
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₇₁×#7289

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₁	#102
commutator	C₂×C₈	C₄²×C₇₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₇₁
socle	C₂²×C₇₁	#340
prime radical	C₂³×C₇₁	#106
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ C₂×C₄×C₈×C₇₁ ◁ G

184 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 119
transitive degree	μ_t(G) = 9088

A minimal faithful permutation representation — 2 generators on 119 points:

(1,2,4,7,5,8,12,15)(3,9,11,16,10,6,13,14)(17,18)(19,28)(20,33)(21,36)(22,38)(23,27)(24,29)(25,35)(26,34)(30,40)(31,48)(32,44)(37,41)(39,47)(42,46)(43,45)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(1,3)(2,6,8,9)(4,11)(5,10)(7,14,15,16)(12,13)(17,19,21,30,34,45,35,46,23,32,20,29,22,31,37,47)(18,24,25,28,38,42,36,48,27,40,41,44,26,39,33,43)

Conjugacy classes & character table

4118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 277);