Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2980 ⋊ C2 |
| Sylow | C79 ⋊ #9333 |
438 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 95 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) = 5056 |
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)(82,89)(84,93)(85,91)(87,90)(88,95)(92,94)(97,103)(99,100)(102,106)(104,105)(107,108)(110,111);(80,82,84,87,85,88,94,81)(83,89,93,90,91,95,92,86)(96,98)(97,102,105,110)(99,107)(100,108)(101,109)(103,106,104,111);(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)(80,81,84,88,85,87,94,82)(83,90,92,95,91,86,93,89)(96,97,100,103,101,105,99,104)(98,106,108,110,109,111,107,102)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,d^2=gh,e^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,d^b=dh,e^b=eg,f^b=fh,d^c=dg,e^c=egh,f^c=fg1516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 66533);