Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #10095 |
480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 5056 |
A minimal faithful permutation representation — 3 generators on 111 points:
(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)(81,86,88,95)(83,92,91,89)(85,93,87,94)(96,98)(97,101)(99,108)(100,105)(102,111)(103,110)(104,106)(107,109);(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)(81,85)(83,91)(86,94)(87,88)(89,92)(93,95)(96,97,100,103)(98,101,105,110)(99,107,106,102)(104,111,108,109);(80,81)(82,86)(83,85)(84,88)(87,91)(89,94)(90,95)(92,93)(98,104)(99,106)(101,109)(102,107)(105,108)(110,111)Polycyclic presentation:
2^8,79|b^2=gh,c^2=g,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fg,c^b=cf,d^b=dg,e^b=egh,i^b=i^78,d^c=dh,e^c=egh1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 70957);