Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #7359 |
176 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 43 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) = 5056 |
A minimal faithful permutation representation — 2 generators on 119 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)(88,90)(89,94,97,111)(91,103)(92,107)(93,101)(95,98,112,115)(96,109,106,110)(99,104)(100,108)(102,113,118,114)(105,117)(116,119);(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)(80,81,82,84,83,85,86,87)(88,89)(90,98,100,113)(91,102,104,118)(92,106,108,96)(93,97)(94,99,109,116)(95,105)(101,115,107,114)(103,110,117,111)(112,119)Polycyclic presentation:
2^8,79|a^2=d,b^2=g,c^2=g,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,c^b=cgh,d^b=degh,e^b=eh,i^b=i^78,d^c=dgh,e^d=eh1048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56960);