Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #12751 |
876 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)(80,83,86,102)(81,88,92,113)(82,94,97,125)(84,100,107,135)(85,103,108,101)(87,109,111,139)(89,112,116,132)(90,117,91,99)(93,119,121,142)(95,123,127,143)(96,129,98,124)(104,131,115,140)(105,133,128,137)(106,136,126,134)(110,138,118,130)(114,122,120,141);(80,82)(81,87)(83,94)(84,105)(85,96)(86,97)(88,109)(89,114)(90,110)(91,118)(92,111)(93,115)(95,126)(98,108)(99,130)(100,133)(101,124)(102,125)(103,129)(104,121)(106,127)(107,128)(112,122)(113,139)(116,120)(117,138)(119,140)(123,134)(131,142)(132,141)(135,137)(136,143);(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)(80,81)(82,93,97,121)(83,99,102,117)(84,104)(85,90)(86,92)(87,95,111,127)(88,101,113,103)(89,106)(91,108)(94,122)(96,120,98,114)(100,132,135,112)(105,118,128,110)(107,115)(109,137)(116,126)(119,129)(123,138)(124,142)(125,141)(130,143)(131,134,140,136)(133,139)Polycyclic presentation:
2^8,79|a^2=f,c^2=h,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^78,d^b=dgh,f^b=fh,g^b=gh,e^c=eh,f^c=fh1756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85313);