Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #455×C97 ⋊ C2 |
| Sylow | C97 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 704 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)(98,102,104,103)(99,107,109,108)(100,112,113,116)(101,114,115,117)(105,110,119,122)(106,120,121,123)(111,126,128,127)(118,124,129,125);(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)(99,106)(100,111)(102,114)(103,117)(104,115)(105,118)(107,120)(108,123)(109,121)(110,124)(112,126)(113,128)(116,127)(119,129)(122,125);(98,100)(99,105)(101,111)(102,112)(103,116)(104,113)(106,118)(107,110)(108,122)(109,119)(114,126)(115,128)(117,127)(120,124)(121,129)(123,125);(98,99,104,109)(100,110,113,122)(101,106,115,121)(102,108,103,107)(105,116,119,112)(111,125,128,124)(114,123,117,120)(118,126,129,127)Polycyclic presentation:
2^7,97|a^2=g,d^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, 13885);