Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #12994 |
530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(85,87)(88,91,94,108)(89,96,99,117)(90,101,105,104)(92,106,93,107)(95,111,114,113)(97,115,98,116)(100,119,112,118)(102,110,103,109);(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)(80,82,83,81)(88,90)(89,95)(91,101)(92,109)(93,110)(94,105)(96,111)(97,118)(98,119)(99,114)(100,115)(102,106)(103,107)(104,108)(112,116)(113,117);(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)(80,81,83,82)(84,85)(86,87)(88,89,93,98,108,117,106,115,94,99,92,97,91,96,107,116)(90,100,103,113,101,119,109,95,105,112,102,111,104,118,110,114)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfgh,c^2=h,d^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,i^a=i^78,d^b=dg,f^b=fg,g^b=gh,i^b=i^781774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86522);