Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #419×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3011 |
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 137 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)(109,120)(113,127)(117,131)(121,133)(125,136)(128,134)(130,137)(132,135);(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)(103,105)(106,109)(107,113)(108,117)(110,121)(111,120)(112,125)(114,128)(115,127)(116,130)(118,132)(119,131)(122,134)(123,135)(124,133)(126,136)(129,137);(106,108,111,119)(107,112,115,126)(109,117,120,131)(110,123,124,118)(113,125,127,136)(114,129,122,116)(121,135,133,132)(128,137,134,130);(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)(104,105)(106,107,111,115)(108,116,119,129)(109,113,120,127)(110,122,124,114)(112,123,126,118)(117,130,131,137)(121,134,133,128)(125,135,136,132)Polycyclic presentation:
2^7,101|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^100,e^b=eg,d^c=dg,h^c=h^1001132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 13806);