Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #12556 |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 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)(62,65,68,81)(63,70,74,73)(64,76,79,92)(66,67,80,82)(69,83,86,85)(71,87,88,72)(75,89,90,84)(77,78,91,93);(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)(58,59,60,61)(62,64,67,78,65,76,80,91,68,79,82,93,81,92,66,77)(63,69,72,84,73,85,88,90,74,86,87,89,70,83,71,75);(54,55,56,57)(62,63)(64,75)(65,70)(66,72)(67,71)(68,74)(69,77)(73,81)(76,89)(78,83)(79,90)(80,87)(82,88)(84,92)(85,93)(86,91)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=h,d^2=gh,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fgh,g^a=gh,i^b=i^521544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84447);