Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #7373 |
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 2 generators on 111 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)(80,82,92,107,85,95,84,94)(81,86,89,101,90,102,87,91)(83,96,98,109,99,108,97,93)(88,104,103,111,106,110,105,100);(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)(80,81,83,88,84,89,98,105,85,90,99,106,92,87,97,103)(82,91,93,104,94,86,96,100,95,101,109,110,107,102,108,111)Polycyclic presentation:
2^8,79|a^2=d,b^2=eg,c^2=gh,d^2=f,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,d^b=deg,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, 56989);