Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #1420 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 generators on 161 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)(98,100,105,116)(99,106,110,132)(101,118,123,147)(102,115,104,113)(103,125,127,145)(107,134,137,143)(108,138,128,130)(109,139,140,141)(111,117,144,154)(112,121,148,158)(114,119,150,126)(120,156,122,155)(124,131,135,160)(129,133,146,157)(136,149,153,161)(142,159,151,152);(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)(98,99,102,108,105,110,104,128)(100,111,113,142,116,144,115,151)(101,117,120,152,123,154,122,159)(103,124,119,140,127,135,126,109)(106,129,130,112,132,146,138,148)(107,133,136,158,137,157,153,121)(114,149,145,134,150,161,125,143)(118,139,155,160,147,141,156,131)Polycyclic presentation:
2^7,97|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^961082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 2702);