Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12613 |
410 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)(80,83,84,97,85,98,100,121,86,99,101,122,102,123,124,139)(81,88,89,107,91,109,111,131,90,108,110,130,112,132,133,142)(82,93,95,117,96,118,120,138,94,116,103,125,119,137,126,140)(87,104,105,127,106,128,129,141,92,113,114,134,115,135,136,143);(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)(80,82)(81,87,90,92)(83,93)(84,95)(85,96)(86,94)(88,104,108,113)(89,105,110,114)(91,106,112,115)(97,117)(98,118)(99,116)(100,120)(101,103)(102,119)(107,127,130,134)(109,128,132,135)(111,129,133,136)(121,138)(122,125)(123,137)(124,126)(131,141,142,143)(139,140);(80,81,84,89,85,91,100,111,86,90,101,110,102,112,124,133)(82,92,95,114,96,115,120,136,94,87,103,105,119,106,126,129)(83,88,97,107,98,109,121,131,99,108,122,130,123,132,139,142)(93,113,117,134,118,135,138,143,116,104,125,127,137,128,140,141)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,f^a=fh,d^b=dh,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, 84664);