Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #454×C97 ⋊ C2 |
| Sylow | C97 ⋊ #3020 |
698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3104 |
A minimal faithful permutation representation — 4 generators on 129 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)(99,106)(104,119)(105,120)(107,114)(108,122)(118,129)(121,123)(124,125);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(98,101,103,113)(99,105,106,120)(100,109,111,127)(102,116,117,112)(104,118,119,129)(107,123,114,121)(108,124,122,125)(110,128,115,126);(98,100)(99,104)(101,109)(102,115)(103,111)(105,118)(106,119)(107,122)(108,114)(110,117)(112,128)(113,127)(116,126)(120,129)(121,124)(123,125);(98,99)(100,108)(101,105)(102,114)(103,106)(104,110)(107,117)(109,125)(111,122)(112,123)(113,120)(115,119)(116,121)(118,126)(124,127)(128,129)Polycyclic presentation:
2^7,97|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^d=h^96797 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 13871);