Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ M128 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 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)(99,105)(106,120)(107,121)(108,122)(109,123)(124,140)(125,141)(126,142)(127,143)(128,144)(129,145)(146,155)(147,156)(148,157)(149,158)(159,161);(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)(98,99,100,106,101,107,110,124,102,108,111,125,114,127,130,146,103,109,112,126,115,128,131,147,117,129,133,148,136,149,150,159,104,105,113,120,116,121,132,140,118,122,134,141,137,143,151,155,119,123,135,142,138,144,152,156,139,145,153,157,154,158,160,161)Polycyclic presentation:
2^7,97|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^963152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 2721);