Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#2141 ⋊ C2 |
| Sylow | C79 ⋊ #13075 |
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 109 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)(80,83)(81,88)(82,94)(84,103)(85,101)(86,100)(87,109)(89,114)(90,98)(91,113)(92,116)(93,121)(95,125)(96,123)(97,124)(99,106)(102,132)(104,133)(105,135)(107,131)(108,134)(110,137)(111,130)(112,115)(117,139)(118,138)(119,136)(120,140)(122,127)(126,141)(128,143)(129,142);(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)(80,82,93,120,85,97,84,95,86,96,105,128,104,126,106,127)(81,87,108,129,91,110,89,92,90,111,102,118,107,117,115,119)(83,94,121,140,101,124,103,125,100,123,135,143,133,141,99,122)(88,109,134,142,113,137,114,116,98,130,132,138,131,139,112,136);(80,81)(82,92)(83,98,100,88)(84,102)(85,107)(86,90)(87,95)(89,105)(91,104)(93,115)(94,116,123,136)(96,119)(97,129)(99,132,103,134)(101,113,133,131)(106,108)(109,122,130,125)(110,120)(111,127)(112,121,114,135)(117,128)(118,126)(124,142,141,138)(137,143,139,140)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfgh,d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,e^b=eh,d^c=dh,f^c=fh,i^c=i^781294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 87019);