Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1953 ⋊ C2 |
| Sylow | C79 ⋊ #13418 |
422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(80,83,84,105,88,108,87,114)(81,90,91,121,95,123,94,127)(82,97,98,130,102,132,101,137)(85,111,109,106,112,107,86,113)(89,115,96,128,119,142,118,138)(92,122,93,103,124,139,110,140)(99,134,133,131,135,104,100,136)(116,120,117,141,126,129,125,143);(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)(80,82,88,102)(81,89,95,119)(83,104,108,134)(84,101,87,98)(85,100,112,133)(86,99,109,135)(90,120,123,129)(91,118,94,96)(92,125,124,117)(93,126,110,116)(97,111,132,107)(103,138,140,128)(105,131,114,136)(106,130,113,137)(115,139,142,122)(121,143,127,141);(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)(82,96)(83,103)(84,94)(85,110)(86,92)(87,91)(88,95)(89,98)(90,106)(93,112)(97,129)(99,116)(100,117)(101,119)(102,118)(104,115)(105,122)(107,127)(108,140)(109,124)(111,121)(113,123)(114,139)(120,132)(125,133)(126,135)(128,131)(130,141)(134,142)(136,138)(137,143)Polycyclic presentation:
2^8,79|b^2=h,c^2=d,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fg,g^a=gh,i^a=i^78,c^b=cf,d^b=dh,e^b=eg,f^b=fgh,g^b=gh,i^b=i^78,e^c=egh,f^c=fg,g^c=gh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88979);