Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#2243 ⋊ C2 |
| Sylow | C79 ⋊ #12388 |
296 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 61 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) = 10112 |
A minimal faithful permutation representation — 3 generators on 127 points:
(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)(80,82,84,89)(81,85,87,94)(83,93,92,90)(86,95,91,88)(96,99,102,101)(97,104,106,116)(98,108,110,117)(100,114,115,111)(103,119,120,121)(105,123,124,112)(107,122,125,126)(109,127,118,113);(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)(83,92)(86,91)(88,95)(90,93)(96,98)(97,103)(99,108)(100,113)(101,117)(102,110)(104,119)(105,122)(106,120)(107,112)(109,114)(111,118)(115,127)(116,121)(123,125)(124,126);(80,81,84,87)(82,88,89,95)(83,91,92,86)(85,93,94,90)(96,97,102,106)(98,107,110,125)(99,104,101,116)(100,112,115,123)(103,118,120,109)(105,111,124,114)(108,126,117,122)(113,119,127,121)Polycyclic presentation:
2^8,79|a^2=g,c^2=g,d^2=fh,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=egh,f^a=fh,d^b=df,e^b=eg,f^b=fh,d^c=dg,e^c=egh,i^c=i^781045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 83485);