Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12829 |
378 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)(80,83)(81,88)(82,93)(84,103)(85,108)(86,98)(87,109)(89,113)(90,116)(91,117)(92,118)(94,126)(95,121)(96,129)(97,101)(99,105)(100,104)(102,136)(106,138)(107,112)(110,141)(111,142)(114,133)(115,143)(119,140)(120,124)(122,128)(123,127)(125,131)(130,134)(132,137)(135,139);(80,82,85,96,86,95,104,127)(81,87,107,119,89,92,91,111)(83,93,108,129,98,121,100,123)(84,102,105,137,106,94,125,128)(88,109,112,140,113,118,117,142)(90,115,134,135,114,110,101,124)(97,120,116,143,130,139,133,141)(99,132,138,126,131,122,103,136);(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)(82,92,95,87)(83,97)(84,101)(85,107)(86,89)(88,99)(90,105)(91,104)(93,120,121,139)(94,124,102,135)(96,111,127,119)(98,130)(100,133)(103,117)(106,134)(108,116)(109,122,118,132)(110,128,115,137)(112,138)(113,131)(114,125)(123,141,129,143)(126,140,136,142)Polycyclic presentation:
2^8,79|a^2=f,b^2=dg,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^78,e^b=eh,f^b=fh,d^c=dh,e^c=eg,g^c=gh1762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85705);