Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#1818 ⋊ C2 |
| Sylow | C79 ⋊ #8540 |
718 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 718 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) = 127 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 127 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)(80,83,84,91)(81,86,87,93)(82,89,90,95)(85,92,88,94)(96,99)(97,103)(98,106)(100,110)(101,109)(102,112)(104,116)(105,115)(107,119)(108,120)(111,122)(113,118)(114,124)(117,126)(121,123)(125,127);(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)(80,82)(81,85)(83,89)(84,90)(86,92)(87,88)(91,95)(93,94)(96,98)(97,102)(99,106)(100,108)(101,107)(103,112)(104,114)(105,113)(109,119)(110,120)(111,121)(115,118)(116,124)(117,125)(122,123)(126,127);(80,81)(82,88,90,85)(83,86)(84,87)(89,94,95,92)(91,93)(96,97,100,104,101,105,111,117)(98,102,108,114,107,113,121,125)(99,103,110,116,109,115,122,126)(106,118,120,127,119,112,123,124)Polycyclic presentation:
2^8,79|a^2=f,c^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^b=eh,f^b=fg,i^b=i^78,d^c=dh1756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62167);