Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #471×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3067 |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 4 generators on 133 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)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,106,108,107)(103,111,113,112)(104,116,118,117)(105,120,121,122)(109,124,125,114)(110,126,127,119)(115,130,131,132)(123,133,129,128);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,105)(103,110)(104,115)(106,120)(107,122)(108,121)(109,123)(111,126)(112,119)(113,127)(114,128)(116,130)(117,132)(118,131)(124,133)(125,129);(102,104,106,116,108,118,107,117)(103,109,112,114,113,125,111,124)(105,115,120,130,121,131,122,132)(110,123,119,128,127,129,126,133);(102,103)(104,114)(105,119)(106,111)(107,112)(108,113)(109,116)(110,120)(115,129)(117,125)(118,124)(121,126)(122,127)(123,131)(128,130)(132,133)Polycyclic presentation:
2^7,101|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,f^c=fg,h^d=h^100832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 14225);