Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #519×C103 ⋊ C2 |
| Sylow | C103 ⋊ #1912 |
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 135 |
| transitive degree | μt(G) = 3296 |
A minimal faithful permutation representation — 3 generators on 135 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(104,107,110,123)(105,112,114,120)(106,116,118,132)(108,122,109,121)(111,125,126,134)(113,128,124,127)(115,129,130,135)(117,133,119,131);(104,106)(105,111,114,126)(107,116)(108,117)(109,119)(110,118)(112,125,120,134)(113,115,124,130)(121,131)(122,133)(123,132)(127,135,128,129);(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)(102,103)(104,105,109,113,110,114,108,124)(106,115,119,126,118,130,117,111)(107,120,122,128,123,112,121,127)(116,129,133,125,132,135,131,134)Polycyclic presentation:
2^7,103|a^2=f,b^2=df,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^102,e^b=eg,d^c=dg,f^c=fg1763 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 5047);