Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13372 |
370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(81,83)(84,86)(85,92)(87,100)(88,103)(89,99)(90,97)(91,106)(93,111)(94,109)(95,110)(96,112)(98,104)(101,115)(102,114)(105,108)(107,113);(80,81)(82,83)(85,91)(86,97,100,99)(92,109,106,110)(93,107)(94,95)(96,113,114,111)(98,103,108,115)(102,112);(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)(84,85,87,91)(86,96)(88,102,101,112)(89,95,90,94)(92,108)(93,104,107,105)(97,113)(98,106)(99,111)(100,114)(103,110)(109,115)Polycyclic presentation:
2^8,79|a^2=d,b^2=dh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^78,c^b=cf,d^c=dh,e^c=egh,f^c=fh,g^c=gh1756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88681);