Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C79×#1452 ⋊ C2 |
| Sylow | C79 ⋊ #9758 |
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 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)(81,85)(84,87)(88,91,92,103,93,104,106,119)(89,95,97,101,96,111,105,117)(90,98,100,113,99,102,114,118)(94,107,108,112,109,110,115,116);(80,81,82,84,83,85,86,87)(88,90)(89,94,96,109)(91,102)(92,100)(93,99)(95,110,111,107)(97,108,105,115)(98,104)(101,116,117,112)(103,118)(106,114)(113,119);(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)(81,84)(82,86)(85,87)(88,89)(90,94,99,109)(91,101)(92,105)(93,96)(95,103)(97,106)(98,112,102,116)(100,115,114,108)(104,117)(107,118,110,113)(111,119)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=e,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,c^b=cg,d^b=dh,f^b=fh2224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 68956);