Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12592 |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 123 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)(84,86,87,90)(85,89,88,91)(94,102)(98,108)(103,114)(104,115)(109,118)(110,119)(116,122)(120,123);(80,81,82,83)(85,88)(89,91)(92,94)(93,98)(95,103)(96,104)(97,102)(99,109)(100,110)(101,108)(105,116)(106,114)(107,115)(111,120)(112,118)(113,119)(117,122)(121,123);(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)(84,85)(86,89)(87,88)(90,91)(92,93,95,99,96,100,105,111,97,101,106,112,107,113,117,121)(94,98,103,109,104,110,116,120,102,108,114,118,115,119,122,123)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=d,e^2=g,g^2=h,b^a=bd,i^a=i^78,c^b=ch3232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84573);