Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #13123 |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 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)(54,57,58,75,61,76,60,78)(55,63,64,88,66,74,79,104)(56,69,70,97,73,98,72,100)(59,77,68,95,81,87,80,106)(62,84,67,91,86,103,93,96)(65,89,83,108,90,105,94,115)(71,99,82,107,102,112,101,109)(85,110,92,113,111,117,114,116);(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)(54,56,68,82,58,70,81,102,61,73,80,101,60,72,59,71)(55,62,83,92,79,93,65,85,66,86,94,114,64,67,90,111)(57,69,95,107,75,97,87,112,76,98,106,109,78,100,77,99)(63,84,108,113,104,96,89,110,74,103,115,116,88,91,105,117);(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)(54,55,59,65,60,64,80,83,61,66,81,90,58,79,68,94)(56,67,71,92,72,86,101,111,73,93,102,114,70,62,82,85)(57,74,77,105,78,104,106,115,76,63,87,89,75,88,95,108)(69,96,99,116,100,84,109,110,98,91,112,113,97,103,107,117)Polycyclic presentation:
2^8,53|a^2=f,b^2=df,c^2=d,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^52,i^b=i^52,e^c=eh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 87319);