Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#108×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2916 |
440 conjugacy classes of subgroups.
| 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)(101,114)(106,120)(110,124)(115,116)(118,128)(121,127)(122,129)(125,126);(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)(99,106)(100,110)(102,115)(103,116)(104,114)(105,118)(107,121)(108,120)(109,122)(111,125)(112,126)(113,124)(117,127)(119,128)(123,129);(98,100,102,111,104,113,103,112)(99,105,107,109,108,119,117,123)(101,110,115,125,114,124,116,126)(106,118,121,122,120,128,127,129);(98,99,103,107,104,108,102,117)(100,109,112,119,113,123,111,105)(101,106,116,121,114,120,115,127)(110,122,126,128,124,129,125,118)Polycyclic presentation:
2^7,97|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,d^c=dg,h^d=h^961388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 13118);