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 ⋊ #11401 |
298 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)(68,78)(70,81)(71,82)(79,88)(80,89)(83,91)(90,93);(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)(55,58)(59,61)(62,64,65,72,66,73,75,84,67,74,76,85,77,86,87,92)(63,68,70,79,71,80,83,90,69,78,81,88,82,89,91,93);(54,55,56,59,57,58,60,61)(62,63)(64,68)(65,70)(66,71)(67,69)(72,79)(73,80)(74,78)(75,83)(76,81)(77,82)(84,90)(85,88)(86,89)(87,91)(92,93)Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,e^2=g,g^2=h,b^a=bf,c^a=ch,i^b=i^522192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 78557);