Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #11840 |
446 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 446 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)(80,82,84,89)(81,86,87,95)(83,91,92,88)(85,93,90,94)(97,102)(101,109)(103,110)(104,111);(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)(81,85)(86,94)(87,90)(93,95)(96,98)(97,101)(99,107)(100,106)(102,109)(103,111)(104,110)(105,108);(80,81)(82,86)(83,90,92,85)(84,87)(88,93,91,94)(89,95)(96,97)(98,104,106,111)(99,103)(100,102)(101,105,109,107)(108,110)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,c^b=cf,d^b=dg,e^b=efg,d^c=dh,i^c=i^78,e^d=eh934 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80428);