Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #7650 |
384 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 119 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) = 20224 |
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)(80,82,84,83)(81,85,86,87)(88,91,92,100)(89,94,95,99)(90,97,98,103)(93,101,96,102)(105,110)(109,117)(111,118)(112,119);(88,90,92,98)(89,93,95,96)(91,97,100,103)(94,101,99,102)(104,106)(105,109)(107,115)(108,114)(110,117)(111,119)(112,118)(113,116);(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)(80,81,83,85,84,86,82,87)(88,89)(90,96,98,93)(91,99)(92,95)(94,100)(97,101,103,102)(104,105)(106,112,114,119)(107,111)(108,110)(109,113,117,115)(116,118)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=fh,d^2=g,e^2=h,b^a=bd,c^a=cfgh,d^a=df,i^a=i^78,d^b=dg,e^b=efg2236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57886);