Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#354×C79 ⋊ C2 |
| Sylow | C79 ⋊ #12763 |
992 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 107 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) = 2528 |
A minimal faithful permutation representation — 3 generators on 99 points:
(7,14)(10,19)(11,16)(15,17)(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);(5,7,9,14)(6,10,12,19)(8,17,18,15)(11,20,16,13)(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);(1,2,3,4)(5,6)(7,13,14,20)(8,16,18,11)(9,12)(10,15)(17,19)Polycyclic presentation:
2^8,79|a^2=f,b^2=h,d^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,c^b=ch,d^b=dh,e^b=egh,f^b=fgh,d^c=dg,i^c=i^78,e^d=eh,f^d=fh1048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85390);