Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1341 ⋊ C2 |
| Sylow | C79 ⋊ #11688 |
432 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 79 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)(80,83,86,85)(81,88,90,101)(82,92,95,94)(84,96,100,99)(87,102,104,103)(89,97,107,106)(91,108,109,105)(93,98,111,110);(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)(81,87)(83,92)(84,98)(85,94)(86,95)(88,102)(89,105)(90,104)(91,97)(93,99)(96,111)(100,110)(101,103)(106,109)(107,108);(80,81,83,88,86,90,85,101)(82,91,94,105,95,109,92,108)(84,97,99,89,100,106,96,107)(87,98,102,111,104,110,103,93)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=gh,e^2=h,f^2=h,g^2=h,b^a=bd,d^a=df,g^a=gh,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,i^c=i^78,e^d=eh820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79728);