Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #1537 |
194 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 6464 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2,5,10,19,32,49,42,25,12,3,7,14,23,36,53,68,59,38,21,8,16,27,40,57,72,83,74,55,34,17,29,44,61,76,87,94,85,70,51,30,46,64,79,90,97,99,92,81,66,47,65,80,91,98,101,100,96,89,78,63,45,62,77,88,95,93,86,75,60,43,28,41,58,73,84,82,71,56,39,26,15,24,37,54,69,67,52,35,22,13,6,11,20,33,50,48,31,18,9,4)(118,121,123,122)(119,125,126,130)(120,128,129,131)(124,132,133,127);(102,104,106,112)(103,107,108,110)(105,113,114,111)(109,117,116,115)(118,120)(119,124)(121,128)(122,131)(123,129)(125,132)(126,133)(127,130);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101)(102,103,105,109,106,108,114,116)(104,110,111,117,112,107,113,115)(118,119)(120,127,129,132)(121,130)(122,125)(123,126)(124,128,133,131)Polycyclic presentation:
2^7,101|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,h^a=h^10,d^b=dg,e^b=efg,h^e=h^100526 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20001);