Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C103 ⋊ #1791 |
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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)(105,111)(106,115)(108,119)(109,118)(110,122)(112,125)(113,124)(114,128)(116,129)(117,130)(120,132)(121,131)(123,133)(126,135)(127,134);(104,106)(105,110)(107,115)(108,120)(109,116)(111,122)(112,114)(113,127)(117,121)(118,129)(119,132)(123,126)(124,134)(125,128)(130,131)(133,135);(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)(104,105,108,113,109,112,121,126)(106,114,117,127,116,110,120,123)(107,111,119,124,118,125,131,135)(115,122,130,133,129,128,132,134)Polycyclic presentation:
2^7,103|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^102,e^b=eg,f^b=fg,d^c=dg1766 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 4461);