Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#1750 ⋊ C2 |
| Sylow | C53 ⋊ #25681 |
1032 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)(58,60,61,65)(59,63,62,64)(67,72)(71,79)(73,78)(77,81);(55,57)(66,68,75,80,70,76,69,74)(67,71,78,81,72,79,73,77);(54,55)(56,57)(59,62)(63,64)(66,67)(68,71)(69,73)(70,72)(74,77)(75,78)(76,79)(80,81);(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)(58,59,61,62)(60,64,65,63)(68,74)(69,75)(71,77)(73,78)(76,80)(79,81)Polycyclic presentation:
2^8,53|a^2=e,c^2=fh,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^52,c^b=cg,d^b=dh1502 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 223938);