Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #11406 |
282 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)(89,95)(90,99)(96,109)(97,110)(100,102)(101,115)(106,116)(112,119);(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)(88,90)(89,94,95,108)(91,102)(92,101)(93,99)(96,111,109,107)(97,98,110,114)(100,104)(103,106)(105,115)(112,117,119,113)(116,118);(88,89,91,96,92,97,103,112,93,95,104,109,105,110,118,119)(90,98,100,113,101,108,116,111,99,114,102,117,115,94,106,107)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,c^a=ch,e^a=eh,c^b=ch,d^b=dh,i^b=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 78576);