Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13688 |
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 147 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)(84,86,90,100)(85,91,95,116)(87,102,106,136)(88,108,110,142)(89,112,109,99)(92,118,120,145)(93,122,123,147)(94,124,111,115)(96,125,127,101)(97,117,113,104)(98,121,130,103)(105,140,138,135)(107,114,141,143)(119,146,132,129)(126,133,131,139)(128,137,134,144);(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)(80,81,82,83);(81,83)(84,85,90,95)(86,96,100,127)(87,101,106,125)(88,107,110,141)(89,111,109,94)(91,113,116,97)(92,117,120,104)(93,121,123,103)(98,129,130,146)(99,131,112,126)(102,122,136,147)(105,139,138,133)(108,118,142,145)(114,140,143,135)(115,128,124,134)(119,137,132,144)Polycyclic presentation:
2^8,79|a^2=h,b^2=d,c^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,e^c=ef,f^c=fg,g^c=gh,i^c=i^781531 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90360);