Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2317 ⋊ C2 |
| Sylow | C53 ⋊ #23634 |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 4 generators on 81 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)(66,68,70,75)(67,72,74,79)(69,76,77,81)(71,78,73,80);(55,57)(58,60,61,64)(59,63,62,65)(67,71)(69,77)(72,78)(73,74)(76,81)(79,80);(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)(59,62)(63,65)(66,67)(68,72)(69,71)(70,74)(73,77)(75,79)(76,78)(80,81);(54,55,56,57)(58,59)(60,63)(61,62)(64,65)(68,75)(72,79)(76,81)(78,80)Polycyclic presentation:
2^8,53|a^2=f,c^2=e,d^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,g^b=gh,i^b=i^52,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, 198378);