Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #8076 |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 5056 |
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)(96,99,101,100)(97,103,105,104)(98,107,109,108)(102,110,111,106);(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)(81,85,87,88)(83,90)(84,89)(86,93,94,95)(91,92)(96,98,100,108,101,109,99,107)(97,102,103,110,105,111,104,106);(80,81,83,86,84,87,91,94)(82,88,90,95,89,85,92,93)(96,97)(98,106)(99,103)(100,104)(101,105)(102,107)(108,111)(109,110)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,d^a=dg,f^a=fgh,d^b=dh,i^b=i^782260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 59795);