Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2214 ⋊ C2 |
| Sylow | C79 ⋊ #12315 |
362 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(80,82)(81,86)(83,97)(84,91)(85,93)(87,106)(88,102)(89,103)(90,95)(92,111)(94,100)(96,101)(98,110)(99,104)(105,109)(107,108);(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)(83,96)(84,100)(87,105)(88,99)(90,108)(91,94)(92,110)(95,107)(97,101)(98,111)(102,104)(106,109);(80,81,85,89)(82,90,93,109)(83,95,98,105)(84,99,100,88)(86,101,103,92)(87,96,107,111)(91,108,94,106)(97,104,110,102)Polycyclic presentation:
2^8,79|a^2=h,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,g^a=gh,d^b=df,e^b=eg,g^b=gh,i^b=i^78,d^c=dg,e^c=egh,f^c=fh,g^c=gh925 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 82985);