Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7093 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 2 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)(80,81,85,87)(82,91,93,95)(83,89,84,88)(86,90,94,92)(96,98)(97,101)(99,103)(100,108)(102,110)(104,109)(105,106)(107,111);(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)(81,86,87,94)(82,90)(83,84)(88,91,89,95)(92,93)(96,97,99,103,109,108,111,106,100,104,110,102,101,98,105,107)Polycyclic presentation:
2^8,79|a^2=d,b^2=g,c^2=fh,d^2=ef,e^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fg,i^a=i^78,c^b=cf,d^b=defg,e^b=eg,f^b=fh1525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56291);