Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #508×D97 |
| Fitting | #508×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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);(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)(98,101,104,103)(99,106,108,118)(100,110,112,119)(102,113,117,116)(105,120,122,121)(107,114,124,128)(109,125,126,123)(111,115,127,129);(98,100)(99,105)(101,110)(102,115)(103,119)(104,112)(106,120)(107,123)(108,122)(109,114)(111,116)(113,127)(117,129)(118,121)(124,125)(126,128);(98,99)(100,109)(101,106)(102,114)(103,118)(104,108)(105,111)(107,116)(110,125)(112,126)(113,124)(115,120)(117,128)(119,123)(121,129)(122,127)1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 17624);