Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7470 |
178 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 2 generators on 121 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)(54,55,56,57)(58,60)(59,66)(61,77)(62,80)(63,75)(64,73)(65,76)(67,90)(68,93)(69,88)(70,72)(71,89)(74,83)(78,101)(79,105)(81,108)(82,86)(84,102)(85,104)(87,96)(91,99)(92,114)(94,116)(95,107)(97,100)(98,113)(103,110)(106,120)(109,111)(112,118)(115,119)(117,121);(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)(58,59,62,68,63,69,81,94,64,70,82,95,84,97,109,117,65,71,83,96,85,98,110,118,61,67,78,91,79,92,106,115)(60,72,74,99,75,100,103,119,73,89,101,93,102,113,120,116,76,90,80,107,104,114,108,121,77,66,86,87,105,88,111,112)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^52,c^b=ch,d^b=dh,i^b=i^522192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57267);