Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #508×C97 ⋊ C2 |
| Sylow | C97 ⋊ #2262 |
106 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 41 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 — 3 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)(98,101,104,119)(99,106,110,109)(100,112,116,115)(102,117,123,150)(103,118,126,151)(105,127,129,137)(107,130,134,133)(108,131,136,124)(111,138,139,146)(113,140,143,142)(114,141,145,125)(120,147,153,152)(121,148,155,154)(122,149,156,159)(128,135,157,161)(132,144,158,160);(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)(99,105)(101,112)(102,121)(103,125)(104,116)(106,127)(107,132)(108,135)(109,137)(110,129)(111,120)(113,122)(114,118)(115,119)(117,148)(123,155)(124,128)(126,141)(130,144)(131,157)(133,160)(134,158)(136,161)(138,147)(139,153)(140,149)(142,159)(143,156)(145,151)(146,152)(150,154);(98,99)(100,111)(101,106)(102,120)(103,124)(104,110)(105,113)(107,122)(108,118)(109,119)(112,138)(114,144)(115,146)(116,139)(117,147)(121,135)(123,153)(125,132)(126,131)(127,140)(128,154)(129,143)(130,149)(133,159)(134,156)(136,151)(137,142)(141,158)(145,160)(148,157)(150,152)(155,161)Polycyclic presentation:
2^7,97|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^961094 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 6817);