Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C101 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 289 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 — 4 generators on 133 points:
(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)(105,116)(109,122)(113,127)(117,129)(120,126)(123,132)(128,130)(131,133);(102,105)(103,109)(104,113)(106,117)(107,116)(108,120)(110,122)(111,123)(112,126)(114,128)(115,127)(118,130)(119,129)(121,131)(124,132)(125,133);(102,104,107,115)(103,108,110,112)(105,113,116,127)(106,118,119,114)(109,120,122,126)(111,125,124,121)(117,130,129,128)(123,133,132,131);(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)(102,103,106,111,107,110,119,124)(104,112,114,125,115,108,118,121)(105,109,117,123,116,122,129,132)(113,126,128,133,127,120,130,131)Polycyclic presentation:
2^7,101|a^2=f,b^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^100,f^b=fg,d^c=dg1741 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 12993);