Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #11245 |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(80,83,84,94,85,95,97,110)(81,87,88,101,89,102,96,109)(82,91,92,106,93,107,108,111)(86,98,90,103,99,100,104,105);(80,82,84,92,85,93,97,108)(81,86,88,90,89,99,96,104)(83,91,94,106,95,107,110,111)(87,100,101,105,102,98,109,103);(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)(82,90)(83,87,95,102)(84,96)(85,89)(86,92)(88,97)(91,105,107,103)(93,104)(94,109,110,101)(98,106,100,111)(99,108)Polycyclic presentation:
2^8,79|a^2=g,b^2=d,c^2=d,d^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^78,c^b=cf,e^b=eh,e^c=eh,g^c=gh1762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 77686);