Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2216 ⋊ C2 |
| Sylow | C79 ⋊ #13666 |
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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:
(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)(81,83)(84,87,90,105)(85,92,96,95)(86,98,102,101)(88,103,109,138)(89,104,112,123)(91,114,116,126)(93,117,122,121)(94,118,125,110)(97,127,128,134)(99,129,113,131)(100,130,133,111)(106,135,140,139)(107,136,142,141)(108,137,119,144)(115,124,143,147)(120,132,145,146);(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)(85,91)(87,98)(88,107)(89,111)(90,102)(92,114)(93,120)(94,124)(95,126)(96,116)(97,106)(99,108)(100,104)(101,105)(103,136)(109,142)(110,115)(112,130)(113,119)(117,132)(118,143)(121,146)(122,145)(123,133)(125,147)(127,135)(128,140)(129,137)(131,144)(134,139)(138,141);(80,81)(82,83)(84,85,90,96)(86,97,102,128)(87,92,105,95)(88,106,109,140)(89,110,112,118)(91,113,116,99)(93,119,122,108)(94,123,125,104)(98,127,101,134)(100,132,133,146)(103,135,138,139)(107,124,142,147)(111,120,130,145)(114,131,126,129)(115,136,143,141)(117,144,121,137)Polycyclic presentation:
2^8,79|a^2=h,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,i^b=i^781531 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90233);