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 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 704 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)(104,108,110,109)(105,113,115,114)(106,118,119,122)(107,120,121,123)(111,116,125,128)(112,126,127,129)(117,132,134,133)(124,130,135,131);(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)(104,107)(105,112)(106,117)(108,120)(109,123)(110,121)(111,124)(113,126)(114,129)(115,127)(116,130)(118,132)(119,134)(122,133)(125,135)(128,131);(104,106)(105,111)(107,117)(108,118)(109,122)(110,119)(112,124)(113,116)(114,128)(115,125)(120,132)(121,134)(123,133)(126,130)(127,135)(129,131);(104,105,110,115)(106,116,119,128)(107,112,121,127)(108,114,109,113)(111,122,125,118)(117,131,134,130)(120,129,123,126)(124,132,135,133)Polycyclic presentation:
2^7,103|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^102,h^d=h^102845 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 13887);