Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #20829 |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 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)(54,56,57,60)(55,59,58,61)(64,74)(69,84)(73,78)(75,76)(83,86)(85,91)(88,92)(89,90);(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)(62,65,66,79,68,81,67,80)(63,70,71,77,72,87,82,93)(64,73,75,89,74,78,76,90)(69,83,85,88,84,86,91,92);(55,58)(59,61)(62,64)(63,69)(65,78)(66,75)(67,76)(68,74)(70,86)(71,85)(72,84)(73,81)(77,92)(79,90)(80,89)(82,91)(83,87)(88,93);(54,55)(56,59)(57,58)(60,61)(62,63,67,71,68,72,66,82)(64,69,76,85,74,84,75,91)(65,77,80,87,81,93,79,70)(73,88,90,86,78,92,89,83)Polycyclic presentation:
2^8,53|a^2=g,c^2=f,d^2=e,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,c^b=ch,d^b=dh,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, 170195);