Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#347×C79 ⋊ C2 |
| Sylow | C79 ⋊ #12608 |
462 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(80,82,83,81)(85,92)(86,97,99,98)(88,102)(91,96,104,107)(93,95)(100,112,113,111)(101,103)(105,115,114,110);(84,86,88,100,89,98,103,112,90,99,102,113,87,97,101,111)(85,91,94,105,95,96,109,110,92,104,106,114,93,107,108,115);(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)(80,81,83,82)(84,85)(86,96,99,107)(87,93)(88,94)(89,95)(90,92)(91,98,104,97)(100,110,113,115)(101,108)(102,106)(103,109)(105,112,114,111)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=e,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^78,c^b=cg,d^b=dh,e^b=eh,f^c=fh1780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84639);