Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C79 ⋊ #11412 |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 10112 |
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)(82,88)(85,91)(89,94)(92,95)(97,103)(102,112)(104,115)(105,116)(113,122)(114,123)(117,125)(124,127);(80,82)(81,85)(83,89)(84,88)(86,92)(87,91)(90,94)(93,95)(96,98,99,106,100,107,109,118,101,108,110,119,111,120,121,126)(97,102,104,113,105,114,117,124,103,112,115,122,116,123,125,127);(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)(80,81,83,86,84,87,90,93)(82,85,89,92,88,91,94,95)(96,97)(98,102)(99,104)(100,105)(101,103)(106,113)(107,114)(108,112)(109,117)(110,115)(111,116)(118,124)(119,122)(120,123)(121,125)(126,127)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=f,e^2=g,g^2=h,c^a=ch,i^a=i^78,c^b=cf3232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 78607);