Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13549 |
238 conjugacy classes of subgroups.
| 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)(86,96)(91,106)(97,116)(98,117)(99,118)(107,126)(108,127)(109,128)(119,136)(120,137)(121,138)(129,141)(130,142)(131,143)(139,146)(144,147);(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)(84,86)(85,91)(87,97)(88,98)(89,99)(90,96)(92,107)(93,108)(94,109)(95,106)(100,119)(101,120)(102,116)(103,121)(104,117)(105,118)(110,129)(111,130)(112,126)(113,131)(114,127)(115,128)(122,139)(123,136)(124,137)(125,138)(132,144)(133,141)(134,142)(135,143)(140,146)(145,147);(84,85,87,92,88,93,100,110,89,94,101,111,103,113,122,132,90,95,102,112,104,114,123,133,105,115,124,134,125,135,140,145)(86,91,97,107,98,108,119,129,99,109,120,130,121,131,139,144,96,106,116,126,117,127,136,141,118,128,137,142,138,143,146,147)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,c^b=ch,i^c=i^785152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89746);