Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7463 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 2 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)(88,89,95,111,91,97,90,94,104,115,99,108,100,106,110,117,93,96,113,119,105,114,102,107,92,98,112,118,103,116,101,109);(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)(80,81,82,84,83,85,86,87)(89,94,96,107)(90,99)(91,103)(92,104)(95,110)(97,111,114,119)(98,117,115,109)(100,105)(101,113)(102,112)(106,118,116,108)Polycyclic presentation:
2^8,79|a^2=d,b^2=ceg,c^2=egh,d^2=f,e^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^78,d^b=dh3172 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57251);