Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #576×C103 ⋊ C2 |
| Sylow | C103 ⋊ #3290 |
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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 — 4 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)(105,112)(106,117)(108,123)(109,124)(110,128)(111,125)(113,132)(114,131)(115,134)(116,118)(119,121)(120,135)(122,126)(127,130)(129,133);(104,107)(105,111)(106,116)(108,122)(109,124)(110,127)(112,125)(113,131)(114,132)(115,134)(117,118)(119,135)(120,121)(123,126)(128,130)(129,133);(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)(104,106)(105,110)(107,121)(108,119)(109,120)(111,128)(112,133)(113,129)(114,130)(115,125)(116,124)(117,122)(118,126)(123,135)(127,132)(131,134);(104,105)(106,115)(107,112)(108,125)(109,114)(110,118)(111,123)(113,126)(116,128)(117,134)(119,130)(120,129)(121,127)(122,132)(124,131)(133,135)Polycyclic presentation:
2^7,103|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,h^b=h^102,f^c=fg,e^d=eg1151 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 16292);