Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C101 ⋊ #1366 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 2 generators on 133 points:
(1,2,5,10,19,32,49,35,22,13,6,11,20,33,50,66,69,54,39,26,15,24,37,52,67,81,84,73,58,43,28,41,56,71,82,92,95,88,77,62,45,60,75,86,93,99,101,97,90,79,64,47,65,80,91,98,100,94,83,68,51,30,46,63,78,89,96,87,72,53,34,17,29,44,59,74,85,76,57,38,21,8,16,27,40,55,70,61,42,25,12,3,7,14,23,36,48,31,18,9,4)(102,104,107,114)(103,108)(105,117,120,122)(106,121,118,116)(109,113)(110,126)(111,130)(112,124)(115,119,131,129)(123,127)(125,132)(128,133);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,64)(36,51,49,60)(40,53,54,56)(44,57,58,52)(46,61,62,50)(55,68,69,75)(59,72,73,71)(63,76,77,67)(65,70,79,66)(74,83,84,86)(78,87,88,82)(80,85,90,81)(89,94,95,93)(91,96,97,92)(98,100,101,99)(102,103,105,110,118,111,129,127,107,112,120,128,106,109,119,125)(104,113,115,126,121,124,117,132,114,130,131,133,116,108,122,123)Polycyclic presentation:
2^7,101|a^2=d,b^2=f,c^2=fg,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^91,c^b=cf,d^b=def,e^b=eg,h^d=h^100373 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19531);