Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #504×C97 ⋊ C2 |
| Sylow | C97 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 4 generators on 161 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)(101,115)(106,129)(111,139)(116,143)(117,144)(126,152)(130,154)(131,148)(137,159)(140,151)(141,149)(145,158)(146,161)(147,155)(153,157)(156,160);(98,101)(99,106)(100,111)(102,116)(103,117)(104,115)(105,126)(107,130)(108,131)(109,129)(110,137)(112,140)(113,141)(114,139)(118,145)(119,146)(120,144)(121,147)(122,143)(123,148)(124,149)(125,151)(127,153)(128,152)(132,155)(133,156)(134,154)(135,157)(136,158)(138,159)(142,160)(150,161);(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)(98,100,104,114)(99,105,109,128)(101,111,115,139)(102,119,122,150)(103,124,120,113)(106,126,129,152)(107,133,134,142)(108,135,123,127)(110,136,138,118)(112,132,125,121)(116,146,143,161)(117,149,144,141)(130,156,154,160)(131,157,148,153)(137,158,159,145)(140,155,151,147);(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)(98,99,104,109)(100,110,114,138)(101,106,115,129)(102,118,122,136)(103,123,120,108)(105,125,128,112)(107,132,134,121)(111,137,139,159)(113,142,124,133)(116,145,143,158)(117,148,144,131)(119,135,150,127)(126,151,152,140)(130,155,154,147)(141,160,149,156)(146,157,161,153)Polycyclic presentation:
2^7,97|a^2=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^96,e^b=ef,f^b=fg,h^b=h^96,d^c=dg1952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 17663);