Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #11706 |
456 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 456 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) = 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)(88,91,94,93)(89,96,99,98)(90,101,103,104)(92,105,109,108)(95,110,111,112)(97,113,115,106)(100,114,116,117)(102,118,119,107);(80,82)(81,84)(83,87)(85,86)(88,90,94,103)(89,95,99,111)(91,104,93,101)(92,107,109,118)(96,112,98,110)(97,114,115,117)(100,106,116,113)(102,105,119,108);(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)(82,86,87,84)(83,85)(88,89)(90,100,103,116)(91,96)(92,106)(93,98)(94,99)(95,102,111,119)(97,105)(101,114,104,117)(107,110,118,112)(108,115)(109,113)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=h,d^2=gh,f^2=h,g^2=h,b^a=bd,d^a=df,f^a=fh,g^a=gh,i^a=i^78,c^b=ch,d^b=dg,e^b=efgh,f^b=fh,g^b=gh1762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79809);