Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#2222 ⋊ C2 |
| Sylow | C79 ⋊ #13702 |
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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:
(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)(81,90)(83,96)(84,104)(85,97)(86,95)(87,98)(88,107)(89,114)(91,121)(92,119)(93,118)(94,120)(99,128)(100,126)(101,131)(102,125)(103,129)(105,132)(106,130)(108,133)(109,136)(110,134)(111,117)(112,135)(113,138)(115,127)(116,139)(122,142)(123,141)(124,140)(137,143);(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)(80,81,89,113,85,92,102,111,84,91,115,123,105,122,83,88,87,94,99,110,106,124,101,109,86,93,116,137,100,108,103,112)(82,90,114,138,97,119,125,117,104,121,127,141,132,142,96,107,98,120,128,134,130,140,131,136,95,118,139,143,126,133,129,135);(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)(81,88)(82,95)(83,99)(84,86)(85,100)(89,103)(90,117)(91,111)(92,123)(93,109)(94,112)(96,127)(97,130)(98,104)(101,115)(102,116)(105,106)(107,118)(108,110)(113,122)(114,131)(119,138)(120,136)(121,135)(124,137)(125,128)(129,139)(133,141)(134,140)(142,143)Polycyclic presentation:
2^8,79|b^2=dfh,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^a=i^78,i^b=i^78,e^c=eh1060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90445);