C₇₉×#13720 #34125409

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₇₉×#13720

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₇₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄²×C₇₉ ◁ C₄×C₈×C₇₉ ◁ C₄×C₁₆×C₇₉ ◁ G

182 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 20224

A minimal faithful permutation representation — 3 generators on 119 points:

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

Conjugacy classes & character table

5530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6708);