Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21078 |
1118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 73 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)(58,62,64,63)(59,60,66,68)(61,70,72,71)(65,67,69,73);(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)(58,61,63,71,64,72,62,70)(59,65,60,67,66,69,68,73);(54,56,57,55)(58,60,62,59,64,68,63,66)(61,67,70,65,72,73,71,69);(54,55,57,56)(58,59)(60,62)(61,69)(63,68)(64,66)(65,72)(67,71)(70,73)Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,c^2=e,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,d^b=dh,f^c=fh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 172138);