Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #11709 |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
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)(88,91,94,93)(89,96,99,98)(90,101,104,103)(92,105,109,108)(95,110,112,111)(97,113,115,106)(100,116,117,114)(102,107,119,118);(80,82)(81,84)(83,87)(85,86)(88,90)(89,95)(91,101)(92,107)(93,103)(94,104)(96,110)(97,114)(98,111)(99,112)(100,113)(102,108)(105,119)(106,117)(109,118)(115,116);(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)(82,86,87,84)(83,85)(88,89,91,96,94,99,93,98)(90,100,103,114,104,117,101,116)(92,106,105,97,109,113,108,115)(95,107,111,102,112,118,110,119)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^78,d^b=dg,e^b=efgh,f^b=fh,g^b=gh1774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79822);