Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #11835 |
340 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 340 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) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 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)(80,82,84,83)(81,85,86,87)(88,91,93,105)(89,95,98,112)(90,100,102,103)(92,104,106,119)(94,107,108,109)(96,110,97,111)(99,114,113,117)(101,115,116,118);(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)(80,81)(82,85)(83,87)(84,86)(88,90,93,102)(89,94,98,108)(91,103,105,100)(92,101,106,116)(95,109,112,107)(96,99,97,113)(104,118,119,115)(110,117,111,114);(81,85)(82,83)(86,87)(88,89,92,97,93,98,106,96)(90,99,101,108,102,113,116,94)(91,95,104,111,105,112,119,110)(100,114,115,109,103,117,118,107)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=gh,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,c^b=ch,d^b=dg,e^b=efg,i^c=i^78,e^d=eh925 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 80401);