C₇₉×#13691 #34125380

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

Aliases

direct product

C₇₉×#13691

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	C₇₉×#2263	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄×C₈×C₇₉ ◁ C₄×C₁₆×C₇₉ ◁ G

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

normal subgroups only

This group has 200 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)(3,16)(4,22)(5,14)(6,28)(7,11)(8,15)(9,18)(10,24)(12,19)(13,20)(17,40)(21,35)(23,55)(25,58)(26,54)(27,45)(29,43)(30,59)(31,34)(32,53)(33,61)(36,60)(37,47)(38,57)(39,50)(41,49)(42,51)(44,56)(46,52)(48,64)(62,63)(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);(1,3,5,18,8,21,7,20)(2,9,11,16,15,13,14,35)(4,17,23,46,26,48,32,25)(6,19,27,49,31,51,30,50)(10,33,36,37,38,43,44,63)(12,34,39,45,42,28,41,59)(22,52,53,40,54,58,55,64)(24,47,56,61,57,62,60,29);(1,4)(2,10)(3,17)(5,23)(6,29)(7,32)(8,26)(9,33)(11,36)(12,40)(13,43)(14,44)(15,38)(16,37)(18,46)(19,24)(20,25)(21,48)(22,28)(27,47)(30,62)(31,61)(34,54)(35,63)(39,58)(41,52)(42,64)(45,55)(49,56)(50,60)(51,57)(53,59)

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, 6679);