Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13558 |
290 conjugacy classes of subgroups.
| 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)(81,89)(88,109)(90,93)(91,112)(92,113)(94,114)(110,117)(111,134)(115,119)(116,120)(118,136)(121,129)(122,137)(135,139)(138,140)(141,143);(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)(80,82)(81,88)(83,99)(84,102)(85,97)(86,95)(87,98)(89,109)(90,114)(91,117)(92,111)(93,94)(96,105)(100,123)(101,127)(103,130)(104,108)(106,124)(107,126)(110,112)(113,134)(115,121)(116,137)(118,139)(119,129)(120,122)(125,132)(128,142)(131,133)(135,136)(138,141)(140,143);(80,81,84,91,85,92,103,118,86,93,104,119,106,120,131,140,87,89,105,112,107,113,132,136,83,90,100,115,101,116,128,138)(82,94,96,121,97,122,125,141,95,109,123,117,124,134,142,139,98,114,102,129,126,137,130,143,99,88,108,110,127,111,133,135)Polycyclic presentation:
2^8,79|a^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,d^b=dh,e^b=eh,i^b=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89778);