Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C101 ⋊ #1858 |
252 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2)(3,8)(4,7)(5,6)(9,18)(10,17)(11,12)(13,16)(14,15)(19,32)(20,31)(21,22)(23,30)(24,25)(26,29)(27,28)(33,50)(34,49)(35,36)(37,48)(38,39)(40,47)(41,42)(43,46)(44,45)(52,69)(53,54)(55,68)(56,67)(57,58)(59,66)(60,61)(62,65)(63,64)(70,83)(71,72)(73,82)(74,81)(75,76)(77,80)(78,79)(84,93)(85,86)(87,92)(88,91)(89,90)(94,99)(95,96)(97,98)(100,101)(102,105)(103,110)(104,114)(106,121)(107,117)(108,118)(109,122)(111,126)(112,127)(113,128)(115,132)(116,131)(119,125)(120,130)(123,133)(124,129);(2,4,5,3)(6,10,11,9)(7,8,14,13)(12,20,21,19)(15,18,24,23)(16,26,27,17)(22,34,35,33)(25,32,38,37)(28,40,41,31)(29,30,44,43)(36,52,53,51)(39,50,54,55)(42,56,57,49)(45,48,60,59)(46,62,63,47)(58,70,71,69)(61,68,72,73)(64,74,75,67)(65,66,78,77)(76,84,85,83)(79,82,86,87)(80,88,89,81)(90,94,95,93)(91,92,96,97)(98,100,101,99)(102,104,107,115,108,116,106,120)(103,109,111,124,112,123,119,113)(105,114,117,132,118,131,121,130)(110,122,126,129,127,133,125,128);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,54,50)(42,49,57,56)(45,59,60,48)(46,47,63,62)(58,69,71,70)(61,73,72,68)(64,67,75,74)(65,77,78,66)(76,83,85,84)(79,87,86,82)(80,81,89,88)(90,93,95,94)(91,97,96,92)(98,99,101,100)(102,103,107,111,108,112,106,119)(104,113,115,109,116,124,120,123)(105,110,117,126,118,127,121,125)(114,129,132,133,131,128,130,122)Polycyclic presentation:
2^7,101|a^2=f,b^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^91,d^b=dg,e^b=eg,h^b=h^10,d^c=dg,h^c=h^100,h^f=h^100307 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20468);