Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #8244 |
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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) = 10112 |
A minimal faithful permutation representation — 3 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)(96,98,100,108,101,106,99,107)(97,103,104,110,105,111,102,109);(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)(80,82,84,90,83,89,91,95)(81,85,87,93,86,88,92,94)(97,102,105,104)(98,106)(103,110,111,109)(107,108);(80,81,83,86)(82,88,89,85)(84,92,91,87)(90,93,95,94)(96,97,100,104,101,105,99,102)(98,103,108,110,106,111,107,109)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=eh,d^2=g,e^2=g,f^2=h,b^a=bd,d^a=dg,f^a=fgh,c^b=cg,d^b=dh,i^c=i^781534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 60585);