Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1568 ⋊ C2 |
| Sylow | C79 ⋊ #11665 |
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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) = 10112 |
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)(81,84)(85,87)(88,91,93,105)(89,95,98,97)(90,100,102,103)(92,104,108,117)(94,109,110,114)(96,111,113,106)(99,115,116,112)(101,107,118,119);(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)(88,90)(89,94)(91,100)(92,107)(93,102)(95,109)(96,112)(97,114)(98,110)(99,111)(101,117)(103,105)(104,118)(106,116)(108,119)(113,115);(80,81,82,85,83,84,86,87)(88,89)(90,99,102,116)(91,95)(92,106)(93,98)(94,101,110,118)(96,104)(97,105)(100,115,103,112)(107,114,119,109)(108,111)(113,117)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,d^b=dfh,e^b=eh,f^b=fh,i^b=i^781762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79628);