Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#2145 ⋊ C2 |
| Sylow | C79 ⋊ #13335 |
536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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)(81,88)(82,93)(84,104)(85,110)(86,101)(87,111)(89,119)(90,116)(91,122)(92,124)(94,131)(95,134)(96,129)(97,102)(98,130)(99,106)(100,105)(103,127)(107,137)(108,117)(109,128)(112,114)(113,143)(115,123)(118,141)(120,138)(121,142)(125,135)(126,139)(132,136)(133,140);(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)(80,82,86,96)(81,87,90,112)(83,93,101,129)(84,103,107,139)(85,109,105,95)(88,114,116,111)(89,118,120,133)(91,121,108,113)(92,123,125,102)(94,130,132,106)(97,135,115,124)(98,136,99,131)(100,134,110,128)(104,127,137,126)(117,142,122,143)(119,140,138,141);(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)(82,92)(83,97)(84,102)(85,108)(86,90)(87,94)(88,99)(89,106)(91,105)(93,111)(95,133)(96,125)(98,116)(100,138)(101,115)(103,121)(104,122)(107,123)(109,118)(110,119)(112,132)(113,139)(114,129)(117,137)(120,130)(124,127)(126,135)(128,143)(131,141)(134,142)(136,140)Polycyclic presentation:
2^8,79|b^2=h,d^2=gh,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^78,c^b=cf,d^b=dg,e^b=eg,g^b=gh,i^b=i^78,d^c=dgh,e^c=eg,g^c=gh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88460);