Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #8488 |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
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)(54,57,58,61)(55,59,60,56)(62,65)(63,70)(64,75)(66,81)(67,79)(68,80)(69,82)(71,87)(72,85)(73,86)(74,88)(76,92)(77,91)(78,90)(83,93)(84,89);(54,56)(55,57)(58,59)(60,61)(62,64)(63,69)(65,75)(66,78)(67,76)(68,77)(70,82)(71,84)(72,74)(73,83)(79,92)(80,91)(81,90)(85,88)(86,93)(87,89);(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)(56,61,59,57)(58,60)(62,63,67,72,68,73,66,71)(64,74,78,69,77,84,76,83)(65,70,79,85,80,86,81,87)(75,89,90,93,91,88,92,82)Polycyclic presentation:
2^8,53|a^2=f,c^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^52,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,f^c=fg1025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 61902);