C₇₉×#13693 #34125382

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#13693

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	#508×C₇₉	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄×C₈×C₇₉ ◁ C₄×C₁₆×C₇₉ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 143
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 143 points:

(1,2,7,12)(3,13,18,43)(4,19,24,52)(5,25,14,10)(6,27,29,58)(8,30,32,16)(9,33,37,21)(11,39,41,17)(15,40,47,64)(20,51,23,50)(22,49,46,63)(26,56,44,42)(28,31,59,62)(34,53,36,54)(35,57,61,45)(38,48,55,60)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143);(1,3,14,30,7,18,5,16)(2,8,25,43,12,32,10,13)(4,15,23,46,24,47,20,22)(6,17,44,60,29,39,26,48)(9,31,36,61,37,62,34,35)(11,27,55,56,41,58,38,42)(19,49,51,64,52,63,50,40)(21,45,54,59,33,57,53,28);(1,4)(2,9)(3,15)(5,20)(6,28)(7,24)(8,31)(10,34)(11,40)(12,37)(13,35)(14,23)(16,22)(17,21)(18,47)(19,27)(25,36)(26,57)(29,59)(30,46)(32,62)(33,39)(38,63)(41,64)(42,50)(43,61)(44,45)(48,53)(49,55)(51,56)(52,58)(54,60)

Conjugacy classes & character table

2923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6681);