Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1464 ⋊ C2 |
| Sylow | C79 ⋊ #8348 |
726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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)(93,102)(94,106)(96,109)(97,108)(98,112)(100,113)(101,114)(104,116)(105,115)(107,117)(110,119)(111,118);(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)(82,86)(83,85)(84,87)(88,90)(89,94)(91,99)(92,104)(93,100)(95,106)(96,98)(97,111)(101,105)(102,113)(103,116)(107,110)(108,118)(109,112)(114,115)(117,119);(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)(81,84,85,86)(88,89,92,97,93,96,105,110)(90,98,101,111,100,94,104,107)(91,95,103,108,102,109,115,119)(99,106,114,117,113,112,116,118)Polycyclic presentation:
2^8,79|a^2=f,d^2=h,f^2=g,b^a=bd,c^a=ce,d^a=dg,i^a=i^78,d^b=dh,e^b=eg,f^b=fgh,i^b=i^78,d^c=dg1294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61091);