Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #11600 |
386 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)(88,91,93,105)(89,95,98,97)(90,100,102,103)(92,104,108,119)(94,109,110,111)(96,112,114,106)(99,113,115,116)(101,117,118,107);(88,90,93,102)(89,94,98,110)(91,103,105,100)(92,107,108,117)(95,111,97,109)(96,113,114,116)(99,106,115,112)(101,104,118,119);(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)(88,89)(90,99,102,115)(91,95)(92,106)(93,98)(94,101,110,118)(96,104)(97,105)(100,113,103,116)(107,109,117,111)(108,112)(114,119)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^78,c^b=ch,d^b=dfh,e^b=eh,f^b=fh2248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79347);