Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #8520 |
976 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 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)(88,91)(89,95)(90,99)(92,103)(93,104)(94,107)(96,109)(97,102)(98,112)(100,114)(101,115)(105,118)(106,119)(108,116)(110,113)(111,117);(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)(81,84)(83,87)(85,86)(88,90,93,101)(89,94,97,108)(91,99,104,115)(92,105,106,100)(95,107,102,116)(96,110,111,98)(103,118,119,114)(109,113,117,112);(80,81)(82,86,87,84)(83,85)(88,89)(90,98,101,110)(91,102,104,95)(92,96)(93,97)(94,100,108,105)(99,113)(103,117,119,109)(106,111)(107,114)(112,115)(116,118)Polycyclic presentation:
2^8,79|a^2=f,b^2=h,d^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,f^b=fgh,i^b=i^78,f^c=fh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62078);