Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #9759 |
370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 5056 |
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)(81,86)(82,89)(87,91)(90,95)(96,99,111,127,101,113,100,112)(97,103,114,125,104,119,105,109)(98,106,121,126,107,110,108,122)(102,115,123,124,117,118,116,120);(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)(80,82,83,90,84,89,92,95)(81,85,87,88,86,93,91,94)(96,98)(97,102,104,117)(99,110)(100,108)(101,107)(103,118,119,115)(105,116,114,123)(106,113)(109,124,125,120)(111,121)(112,126)(122,127);(80,81)(82,88)(83,91)(84,86)(85,90)(87,92)(89,94)(93,95)(96,97)(98,102,107,117)(99,109)(100,114)(101,104)(103,112)(105,111)(106,120,110,124)(108,123,121,116)(113,125)(115,126,118,122)(119,127)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=eg,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cg,d^b=dh,f^b=fh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 68958);