Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1418 ⋊ C2 |
| Sylow | C79 ⋊ #13622 |
294 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 294 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)(80,83,87,86)(81,89,92,109)(82,94,96,110)(84,98,104,103)(85,99,108,107)(88,111,112,114)(90,115,118,137)(91,105,120,117)(93,122,124,126)(95,127,130,141)(97,106,132,129)(100,134,121,139)(101,135,131,140)(102,136,128,138)(113,123,142,119)(116,133,125,143);(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)(81,88)(83,94)(84,101)(85,106)(86,110)(87,96)(89,111)(90,116)(91,119)(92,112)(93,121)(95,128)(97,107)(98,135)(99,132)(100,124)(102,130)(103,140)(104,131)(105,113)(108,129)(109,114)(115,133)(117,142)(118,125)(120,123)(122,139)(126,134)(127,138)(136,141)(137,143);(80,81)(82,93,96,124)(83,89)(84,100)(85,105)(86,109)(87,92)(88,95,112,130)(90,102)(91,107)(94,122,110,126)(97,133,132,143)(98,134)(99,120)(101,119,131,123)(103,139)(104,121)(106,125,129,116)(108,117)(111,127,114,141)(113,140,142,135)(115,136)(118,128)(137,138)Polycyclic presentation:
2^8,79|a^2=e,c^2=h,d^2=fgh,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,d^b=dfh,e^b=eh,f^b=fg,g^b=gh,i^c=i^781066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90029);