Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C101 ⋊ #1747 |
200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 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:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(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)(102,105,106,116,107,117,118,129)(103,109,110,121,111,122,123,131)(104,113,114,126,115,127,128,133)(108,119,112,124,120,130,125,132);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,104)(103,108,111,120)(105,113)(106,114)(107,115)(109,119,122,130)(110,112,123,125)(116,126)(117,127)(118,128)(121,124,131,132)(129,133);(102,103)(104,112,115,125)(105,109)(106,110)(107,111)(108,114,120,128)(113,124,127,132)(116,121)(117,122)(118,123)(119,126,130,133)(129,131)Polycyclic presentation:
2^7,101|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,e^b=eg,h^c=h^1001144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 4264);