Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2117 ⋊ C2 |
| Sylow | C79 ⋊ #12752 |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
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)(80,83)(81,86)(82,92)(84,98)(85,89)(87,96)(88,102)(90,97)(91,107)(93,109)(94,103)(95,104)(99,111)(100,108)(101,106)(105,110);(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)(80,82)(81,87)(83,92)(84,100)(85,94)(86,96)(88,105)(89,103)(90,104)(91,106)(93,111)(95,97)(98,108)(99,109)(101,107)(102,110);(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)(80,81,85,89,86,83,97,90)(82,91,95,105,96,109,94,108)(84,99,101,88,102,106,111,98)(87,100,104,93,92,110,103,107)Polycyclic presentation:
2^8,79|a^2=f,d^2=g,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^78,d^b=dgh,f^b=fh,g^b=gh,i^b=i^78,e^c=eh,f^c=fh1756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85322);