C₇₉×#13669 #34125358

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13669
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#13669

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ #131×C₇₉ ◁ #504×C₇₉ ◁ G

288 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 74 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)(3,14)(4,20)(5,26)(6,28)(7,13)(8,15)(9,16)(10,24)(11,27)(12,22)(17,37)(18,39)(19,38)(21,43)(23,31)(25,52)(29,40)(30,60)(32,46)(33,54)(34,45)(35,47)(36,53)(41,64)(42,59)(44,57)(48,61)(49,63)(50,58)(51,56)(55,62)(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)(2,8)(4,21)(5,16)(6,29)(7,19)(9,31)(10,40)(11,32)(12,43)(13,35)(14,20)(15,24)(17,22)(18,27)(23,53)(25,55)(26,34)(28,33)(30,48)(36,60)(37,51)(38,52)(39,50)(41,63)(42,61)(44,62)(45,56)(46,64)(47,59)(49,57)(54,58);(1,3)(2,9)(4,15)(5,18)(6,17)(7,19)(8,31)(10,36)(11,38)(12,37)(13,39)(14,26)(16,27)(20,34)(21,24)(22,29)(23,46)(25,47)(28,61)(30,49)(32,52)(33,42)(35,50)(40,60)(41,62)(43,51)(44,63)(45,58)(48,57)(53,64)(54,56)(55,59)

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, 6657);