Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13690 |
204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 147 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)(84,86,87,97)(85,92,91,113)(88,105,101,132)(89,110,102,135)(90,112,103,100)(93,118,114,144)(94,120,115,145)(95,121,111,117)(96,123,122,104)(98,127,125,107)(99,130,126,106)(108,142,133,139)(109,116,134,143)(119,147,136,129)(124,137,131,141)(128,140,138,146);(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)(80,81,82,83)(85,91)(92,113)(93,114)(94,115)(95,111)(96,122)(104,123)(109,134)(116,143)(117,121)(118,144)(119,136)(120,145)(124,131)(129,147)(137,141);(81,83)(84,85)(86,96)(87,91)(88,104)(89,109)(90,111)(92,98)(93,107)(94,106)(95,103)(97,122)(99,129)(100,131)(101,123)(102,134)(105,120)(108,141)(110,118)(112,124)(113,125)(114,127)(115,130)(116,139)(117,138)(119,146)(121,128)(126,147)(132,145)(133,137)(135,144)(136,140)(142,143)Polycyclic presentation:
2^8,79|b^2=dh,c^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,e^c=ef,f^c=fg,g^c=gh,i^c=i^781531 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90372);