Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C79×#1358 ⋊ C2 |
| Sylow | C79 ⋊ #11993 |
360 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 69 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 — 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)(81,87)(83,96)(86,100)(88,90)(91,102)(92,109)(95,110)(97,107);(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)(80,82,85,94)(81,86,87,100)(83,95,96,110)(84,98,99,93)(88,102,90,91)(89,105,103,108)(92,97,109,107)(101,104,111,106);(80,81,83,89,84,88,97,104,85,87,96,103,99,90,107,106)(82,91,92,108,93,100,110,111,94,102,109,105,98,86,95,101)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,d^2=g,e^2=fg,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,e^c=eh,i^c=i^78925 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81101);