Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #456×C103 ⋊ C2 |
| Sylow | C103 ⋊ #3020 |
698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 133 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)(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)(105,112)(110,125)(111,126)(113,120)(114,128)(124,135)(127,129)(130,131);(104,107,109,119)(105,111,112,126)(106,115,117,133)(108,122,123,118)(110,124,125,135)(113,129,120,127)(114,130,128,131)(116,134,121,132);(104,106)(105,110)(107,115)(108,121)(109,117)(111,124)(112,125)(113,128)(114,120)(116,123)(118,134)(119,133)(122,132)(126,135)(127,130)(129,131);(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)(106,114)(107,111)(108,120)(109,112)(110,116)(113,123)(115,131)(117,128)(118,129)(119,126)(121,125)(122,127)(124,132)(130,133)(134,135)Polycyclic presentation:
2^7,103|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^102,e^b=eg,f^b=fg,e^c=eg,h^d=h^102845 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 13875);