C₇₉×#33981 #34145670

order	20224
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₉×#33981

Subgroups

	subgroup	G/H
center	C₄×C₇₉	C₂×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₇₉
socle	C₂×C₇₉	C₂²×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₈×C₇₉ ◁ C₂²×C₁₆×C₇₉ ◁ G

466 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 202 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 — 4 generators on 143 points:

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

Conjugacy classes & character table

4108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 26969);