Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1833 ⋊ C2 |
| Sylow | C79 ⋊ #12830 |
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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)(82,94)(84,104)(85,101)(86,110)(87,99)(88,111)(90,117)(91,120)(92,115)(93,121)(95,128)(96,125)(97,123)(98,102)(100,106)(103,136)(105,132)(107,138)(108,126)(109,116)(112,141)(113,140)(114,142)(118,130)(119,143)(122,127)(124,129)(131,134)(133,137)(135,139);(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)(80,82,86,96,87,97,85,108)(81,88,109,113,90,93,92,114)(83,94,110,125,99,123,101,126)(84,103,106,137,107,95,105,129)(89,111,116,140,117,121,115,142)(91,119,134,135,118,112,102,127)(98,122,120,143,131,139,130,141)(100,133,138,128,132,124,104,136);(80,81,85,92,87,90,86,109)(82,93,96,114,97,88,108,113)(83,98,101,130,99,131,110,120)(84,102,105,118,107,134,106,91)(89,104,115,132,117,138,116,100)(94,122,125,143,123,139,126,141)(95,127,129,119,103,135,137,112)(111,128,140,124,121,136,142,133)Polycyclic presentation:
2^8,79|a^2=f,b^2=dg,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,e^b=eh,f^b=fh,d^c=dh,e^c=eg,g^c=gh,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, 85709);