Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C97 ⋊ C2 |
| Sylow | C97 ⋊ #3584 |
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 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 — 5 generators on 129 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(98,102,104,103)(99,107,108,116)(100,111,112,117)(101,114,113,115)(105,119,120,109)(106,122,121,126)(110,125,124,127)(118,129,128,123);(101,113)(106,121)(110,124)(114,115)(118,128)(122,126)(123,129)(125,127);(98,101)(99,106)(100,110)(102,114)(103,115)(104,113)(105,118)(107,122)(108,121)(109,123)(111,125)(112,124)(116,126)(117,127)(119,129)(120,128);(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)(98,100)(99,105)(101,110)(102,111)(103,117)(104,112)(106,118)(107,119)(108,120)(109,116)(113,124)(114,125)(115,127)(121,128)(122,129)(123,126);(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)(100,109)(101,106)(102,107)(103,116)(104,108)(105,111)(110,123)(112,119)(113,121)(114,122)(115,126)(117,120)(118,125)(124,129)(127,128)Polycyclic presentation:
2^7,97|e^2=g,f^2=g,b^a=bf,f^a=fg,h^a=h^96,f^b=fg,h^b=h^96,d^c=dg1964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 19284);