Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #11406 |
282 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)(63,69)(64,73)(70,83)(71,84)(74,76)(75,89)(80,90)(86,93);(54,55,56,58,57,59,60,61)(62,64)(63,68,69,82)(65,76)(66,75)(67,73)(70,85,83,81)(71,72,84,88)(74,78)(77,80)(79,89)(86,91,93,87)(90,92);(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)(62,63,65,70,66,71,77,86,67,69,78,83,79,84,92,93)(64,72,74,87,75,82,90,85,73,88,76,91,89,68,80,81)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,c^a=ch,e^a=eh,i^a=i^52,c^b=ch,d^b=dh2168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78577);