Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#355×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13055 |
680 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 680 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) = 99 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 99 points:
(6,12)(7,9)(8,17)(11,19)(13,20)(14,15)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(1,3,4,2)(6,11)(7,9)(12,19)(13,15)(14,20)(16,18)(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)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99);(1,2,4,3)(5,6,9,11,10,15,7,13)(8,12,16,19,17,14,18,20)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,e^a=egh,g^a=gh,d^b=dh,e^b=egh,f^b=fh,i^b=i^78,d^c=dg,e^c=eh,f^c=fg,e^d=eh,f^e=fh1048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86908);