Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1425 ⋊ C2 |
| Sylow | C79 ⋊ #13636 |
178 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 79 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:
(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)(82,95)(88,110)(93,117)(96,124)(97,99)(98,125)(109,127)(111,136)(112,138)(118,139)(119,130)(120,140)(121,141)(126,128)(129,143)(137,142);(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)(80,82,94,121,85,98,102,109,84,97,113,137,105,128,104,124,87,95,123,141,107,125,103,127,86,99,122,142,101,126,83,96)(81,88,100,120,91,112,132,130,108,136,134,143,135,139,115,117,92,110,133,140,116,138,114,119,90,111,131,129,106,118,89,93);(80,81,84,90,87,92,86,108)(82,93,97,119,95,117,99,130)(83,100,102,131,104,133,103,134)(85,106,105,116,107,135,101,91)(88,109,111,124,110,127,136,96)(89,113,114,123,115,122,132,94)(98,129,128,140,125,143,126,120)(112,121,118,137,138,141,139,142)Polycyclic presentation:
2^8,79|a^2=e,b^2=df,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,c^b=ch,i^c=i^781534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90080);