Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #10900 |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(80,82,83,81)(84,87)(85,92)(86,96)(88,101)(89,102)(90,103)(91,105)(93,108)(94,109)(95,110)(97,112)(98,114)(99,113)(100,104)(106,115)(107,111);(84,86,89,97,90,99,88,98)(85,91,93,106,94,107,104,95)(87,96,102,112,103,113,101,114)(92,105,108,115,109,111,100,110);(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)(80,81,83,82)(84,85)(86,95)(87,100)(88,104)(89,93)(90,94)(91,97)(92,102)(96,111)(98,107)(99,106)(101,109)(103,108)(105,113)(110,112)(114,115)Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=f,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^78,d^b=dh,e^c=eh2716 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 75677);