Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C97 ⋊ #2950 |
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 4 generators on 133 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)(103,110)(105,116)(108,122)(111,118)(112,125)(113,127)(117,129)(128,131);(98,100,101,99)(102,105,107,116)(103,109,110,124)(104,113,115,127)(106,117,120,129)(108,121,122,132)(111,123,118,130)(112,126,125,133)(114,128,119,131);(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)(102,104,107,115)(103,108,110,122)(105,113,116,127)(106,119,120,114)(109,121,124,132)(111,125,118,112)(117,131,129,128)(123,133,130,126);(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)(98,99,101,100)(102,103)(104,112)(105,109)(106,118)(107,110)(108,114)(111,120)(113,126)(115,125)(116,124)(117,130)(119,122)(121,128)(123,129)(127,133)(131,132)Polycyclic presentation:
2^7,97|a^2=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^96,e^b=eg,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, 13379);