Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #443×C101 ⋊ C2 |
| Sylow | C101 ⋊ #2957 |
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)(103,111)(105,117)(109,123)(112,120)(113,124)(114,128)(118,119)(129,131);(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)(102,105,107,119,108,117,106,118)(103,110,112,125,111,126,120,130)(104,114,115,129,116,128,121,131)(109,122,124,132,123,133,113,127);(102,104)(103,109)(105,114)(106,121)(107,115)(108,116)(110,122)(111,123)(112,124)(113,120)(117,128)(118,131)(119,129)(125,132)(126,133)(127,130);(102,103,107,112,108,111,106,120)(104,113,115,109,116,124,121,123)(105,110,119,125,117,126,118,130)(114,127,129,122,128,132,131,133)Polycyclic presentation:
2^7,101|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,d^c=dg,h^d=h^1001444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 13422);