Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C79×#2253 ⋊ C2 |
| Sylow | C79 ⋊ #12464 |
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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)(81,89)(82,96)(84,102)(85,109)(86,103)(87,105)(88,112)(90,117)(91,122)(92,118)(93,120)(94,123)(95,128)(97,130)(98,135)(99,131)(100,133)(101,121)(104,107)(106,137)(108,116)(110,119)(111,138)(113,141)(114,129)(115,140)(124,139)(125,142)(126,136)(127,143)(132,134);(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)(80,82,95,127,86,99,84,97,87,100,85,98,107,134,108,111)(81,88,91,113,92,114,90,94,93,115,106,125,110,124,121,126)(83,96,128,143,103,131,102,130,105,133,109,135,104,132,116,138)(89,112,122,141,118,129,117,123,120,140,137,142,119,139,101,136);(80,81,87,93)(82,94,100,126)(83,101)(84,106,108,91)(85,90,95,121)(86,110,107,92)(88,111,115,97)(89,116)(96,129)(98,124,127,114)(99,113,134,125)(102,120)(103,137)(104,122)(105,117)(109,118)(112,131)(119,128)(123,138)(130,136)(132,140)(133,139)(135,142)(141,143)Polycyclic presentation:
2^8,79|a^2=fg,b^2=dfh,d^2=fh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,e^c=egh,g^c=gh,i^c=i^781519 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 83963);