Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| automorphism | Aut(G) order 425920 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic484 |
| Sylow | C121 ⋊ Q16 |
27 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 1936 |
A minimal faithful permutation representation — 2 generators on 137 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,137)(19,136)(20,135)(21,134)(22,133)(23,132)(24,131)(25,130)(26,129)(27,128)(28,127)(29,126)(30,125)(31,124)(32,123)(33,122)(34,121)(35,120)(36,119)(37,118)(38,117)(39,116)(40,115)(41,114)(42,113)(43,112)(44,111)(45,110)(46,109)(47,108)(48,107)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,96)(60,95)(61,94)(62,93)(63,92)(64,91)(65,90)(66,89)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)Polycyclic presentation:
2^4,11^2|a^2=d,b^2=cd,c^2=d,e^11=f,b^a=bc,c^a=cd,e^a=e^10f^10,f^a=f^10487 conjugacy classes — view the full character table.
| maximal subgroup of | Dic968, Dic1452, Dic2420, … |
| maximal normal subgroup of | Dic968 |
| maximal quotient of | Dic1452, Dic2420, Dic3388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 3);