Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#1422 ⋊ C2 |
| Sylow | C53 ⋊ #7447 |
130 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 2 generators on 117 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)(54,56)(55,63)(57,77)(58,73)(59,84)(60,87)(61,89)(62,75)(64,94)(65,99)(66,90)(67,91)(68,100)(69,93)(70,96)(71,80)(72,85)(74,83)(76,102)(78,105)(79,113)(81,115)(82,111)(86,116)(88,92)(95,103)(97,101)(98,117)(104,112)(106,114)(107,109)(108,110);(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)(54,55,58,65,83,68,85,66,62,69,59,67,61,88,60,86)(56,70,72,94,89,102,73,107,75,103,87,117,74,108,84,101)(57,76,78,98,112,96,114,109,82,110,79,64,81,95,80,97)(63,77,90,106,92,115,99,105,93,111,116,71,100,104,91,113)Polycyclic presentation:
2^8,53|a^2=d,c^2=fgh,d^2=efg,e^2=gh,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fg,g^a=gh,i^a=i^52,c^b=cf,d^b=defg,e^b=eg,f^b=fgh,g^b=gh,i^b=i^521493 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57211);