Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C101 ⋊ #2960 |
364 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 125 points:
(1,2)(3,8)(4,6)(5,7)(9,18)(10,12)(11,17)(13,16)(14,15)(19,32)(20,22)(21,31)(23,30)(24,25)(26,28)(27,29)(33,50)(34,36)(35,49)(37,48)(38,39)(40,42)(41,47)(43,46)(44,45)(52,54)(53,69)(55,68)(56,58)(57,67)(59,66)(60,61)(62,64)(63,65)(70,72)(71,83)(73,82)(74,76)(75,81)(77,80)(78,79)(84,86)(85,93)(87,92)(88,90)(89,91)(94,96)(95,99)(97,98)(100,101)(111,116)(115,121)(117,123)(122,125);(2,5,4,3)(6,11,10,9)(7,8,14,13)(12,21,20,19)(15,18,24,23)(16,27,26,17)(22,35,34,33)(25,32,38,37)(28,41,40,31)(29,30,44,43)(36,53,52,51)(39,50,54,55)(42,57,56,49)(45,48,60,59)(46,63,62,47)(58,71,70,69)(61,68,72,73)(64,75,74,67)(65,66,78,77)(76,85,84,83)(79,82,86,87)(80,89,88,81)(90,95,94,93)(91,92,96,97)(98,101,100,99)(110,112,113,118,114,119,120,124)(111,115,117,122,116,121,123,125);(2,4)(3,5)(6,10)(7,14)(8,13)(9,11)(12,20)(15,24)(16,26)(17,27)(18,23)(19,21)(22,34)(25,38)(28,40)(29,44)(30,43)(31,41)(32,37)(33,35)(36,52)(39,54)(42,56)(45,60)(46,62)(47,63)(48,59)(49,57)(50,55)(51,53)(58,70)(61,72)(64,74)(65,78)(66,77)(67,75)(68,73)(69,71)(76,84)(79,86)(80,88)(81,89)(82,87)(83,85)(90,94)(91,96)(92,97)(93,95)(98,100)(99,101)(102,104,105,109)(103,106,107,108);(2,3,4,5)(6,9,10,11)(7,13,14,8)(12,19,20,21)(15,23,24,18)(16,17,26,27)(22,33,34,35)(25,37,38,32)(28,31,40,41)(29,43,44,30)(36,51,52,53)(39,55,54,50)(42,49,56,57)(45,59,60,48)(46,47,62,63)(58,69,70,71)(61,73,72,68)(64,67,74,75)(65,77,78,66)(76,83,84,85)(79,87,86,82)(80,81,88,89)(90,93,94,95)(91,97,96,92)(98,99,100,101)(102,103,105,107)(104,108,109,106)(110,111,113,117,114,116,120,123)(112,115,118,122,119,121,124,125)Polycyclic presentation:
2^7,101|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^91,h^b=h^100,h^c=h^10,h^d=h^100,h^f=h^100406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 21300);