Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1389 ⋊ C2 |
| Sylow | C79 ⋊ #13500 |
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 81 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)(80,83,86,102)(81,88,91,116)(82,93)(84,103,105,100)(85,107,108,139)(87,110)(89,117,119,115)(90,121,122,138)(92,123)(94,128)(95,130)(96,126)(97,99)(98,132,133,118)(101,136,137,104)(106,141)(109,127)(111,125)(112,142)(113,114)(120,134)(124,143)(129,135)(131,140);(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)(80,82)(81,87)(83,99)(84,96)(85,106)(86,97)(88,114)(89,112)(90,120)(91,113)(92,119)(93,102)(94,105)(95,108)(98,131)(100,126)(101,127)(103,128)(104,129)(107,130)(109,136)(110,116)(111,122)(115,142)(117,123)(118,124)(121,125)(132,140)(133,143)(134,138)(135,137)(139,141);(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)(80,81,85,90,105,119,136,132,86,91,108,122,84,89,104,118)(82,92,95,124,94,113,129,120,97,112,106,140,96,87,109,111)(83,98,101,117,103,138,139,116,102,133,137,115,100,121,107,88)(93,125,127,110,126,131,141,142,99,134,135,114,128,143,130,123)Polycyclic presentation:
2^8,79|a^2=e,c^2=dg,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,i^a=i^78,c^b=cf,d^b=dh,e^b=eh,i^b=i^78,d^c=dh,e^c=eg,f^c=fh,g^c=gh1288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89473);