Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #100×C101 ⋊ C4 |
| Sylow | C101 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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:
(1,2,7,3)(4,6,17,13)(5,8,15,9)(10,12,31,27)(11,18,25,19)(14,16,29,23)(20,22,49,41)(21,32,39,33)(24,30,45,37)(26,28,47,43)(34,36,52,54)(35,50,57,51)(38,48,61,55)(40,42,67,63)(44,46,65,59)(53,69,72,58)(56,68,75,70)(60,66,79,73)(62,64,81,77)(71,83,86,76)(74,82,89,84)(78,80,91,87)(85,93,96,90)(88,92,98,94)(95,99,100,97)(102,105,106,116,107,117,118,129)(103,109,110,122,111,123,124,132)(104,113,115,128,114,127,119,130)(108,120,121,131,112,125,126,133);(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)(39,50,56,55)(42,58,54,49)(45,48,60,59)(46,62,63,47)(57,69,71,70)(61,68,74,73)(64,76,72,67)(65,66,78,77)(75,83,85,84)(79,82,88,87)(80,90,86,81)(89,93,95,94)(91,92,97,96)(98,99,101,100)(102,104)(103,108,111,112)(105,113)(106,115)(107,114)(109,120,123,125)(110,121,124,126)(116,128)(117,127)(118,119)(122,131,132,133)(129,130);(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)(39,55,56,50)(42,49,54,58)(45,59,60,48)(46,47,63,62)(57,70,71,69)(61,73,74,68)(64,67,72,76)(65,77,78,66)(75,84,85,83)(79,87,88,82)(80,81,86,90)(89,94,95,93)(91,96,97,92)(98,100,101,99)(102,103,106,110,107,111,118,124)(104,112,115,126,114,108,119,121)(105,109,116,122,117,123,129,132)(113,125,128,133,127,120,130,131)Polycyclic presentation:
2^7,101|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,h^a=h^10,d^b=dg,h^b=h^91,h^c=h^10,h^e=h^100,h^f=h^100319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20267);