Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #23646 |
906 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)(62,66,68,67)(63,71,73,72)(64,75,76,82)(65,79,81,80)(69,84,85,89)(70,87,88,77)(74,90,91,78)(83,93,92,86);(54,56,57,60)(55,59,58,61)(62,65)(63,70)(64,74)(66,79)(67,80)(68,81)(69,83)(71,87)(72,77)(73,88)(75,90)(76,91)(78,82)(84,93)(85,92)(86,89);(55,58)(59,61)(62,64)(63,69)(65,78)(66,75)(67,82)(68,76)(70,86)(71,84)(72,89)(73,85)(74,79)(77,92)(80,91)(81,90)(83,87)(88,93);(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)(54,55)(56,59)(57,58)(60,61)(62,63,66,71,68,73,67,72)(64,69,75,84,76,85,82,89)(65,77,80,88,81,87,79,70)(74,86,78,92,91,93,90,83)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,d^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,i^a=i^52,c^b=cg,g^b=gh,f^c=fh,g^c=gh1196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 198473);