C₇₉×#13657 #34125346

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#13657

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2177
commutator	C₁₆	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	#508×C₇₉	C₂²
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄×C₈×C₇₉ ◁ #346×C₇₉ ◁ G

182 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 82 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:

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

Conjugacy classes & character table

2686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6645);