Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C79×#1410 ⋊ C2 |
| Sylow | C79 ⋊ #13589 |
408 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 59 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)(80,83,85,97)(81,87,90,88)(82,92,95,94)(84,96,100,99)(86,91,103,102)(89,104,107,105)(93,108,109,98)(101,106,111,110);(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)(81,86)(83,92)(84,98)(85,95)(87,91)(88,102)(89,106)(90,103)(93,96)(94,97)(99,109)(100,108)(101,105)(104,111)(107,110);(80,81,84,89,85,90,100,107)(82,91,93,106,95,102,109,110)(83,87,96,104,97,88,99,105)(86,98,101,92,103,108,111,94)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=gh,e^2=h,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=dgh,e^b=efg,f^b=fh,i^c=i^78,e^d=egh,f^e=fh697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89897);