Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#1830 ⋊ C2 |
| Sylow | C53 ⋊ #31419 |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,58,60,78)(55,63,65,91)(56,68,69,76)(57,72,74,107)(59,82,83,77)(61,85,66,90)(62,88,89,113)(64,94,79,75)(67,96,97,105)(70,102,80,100)(71,104,93,112)(73,108,81,106)(84,110,87,111)(86,109,92,99)(95,114,103,117)(98,116,101,115);(54,57)(55,62)(56,67,69,97)(58,72)(59,81)(60,74)(61,84,66,87)(63,88)(64,93)(65,89)(68,96,76,105)(70,101,80,98)(71,79)(73,83)(75,104)(77,108)(78,107)(82,106)(85,110,90,111)(86,95,92,103)(91,113)(94,112)(99,117,109,114)(100,116,102,115);(54,56,59,80,60,69,83,70)(55,61,64,92,65,66,79,86)(57,67,73,101,74,97,81,98)(58,76,77,100,78,68,82,102)(62,87,71,103,89,84,93,95)(63,90,75,99,91,85,94,109)(72,105,106,115,107,96,108,116)(88,110,112,117,113,111,104,114);(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)(56,66)(57,71)(58,75)(59,79)(60,65)(61,69)(62,73)(63,77)(64,83)(67,95)(68,99)(70,86)(72,88)(74,93)(76,109)(78,94)(80,92)(81,89)(82,91)(84,101)(85,100)(87,98)(90,102)(96,110)(97,103)(104,106)(105,111)(107,113)(108,112)(114,116)(115,117)Polycyclic presentation:
2^8,53|b^2=ef,c^2=e,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=def,f^a=fh,g^a=gh,i^a=i^52,c^b=cg,d^b=de,e^b=eh,f^b=fh,g^b=gh,f^c=fh,g^c=gh,f^d=fh788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 298016);