Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #106 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,16,17)(19,22)(20,24)(23,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(18,19,20,22,21,23,24,25)Polycyclic presentation:
2^5,13|a^2=d,b^2=c,d^2=e,b^a=bde,f^a=f^12,d^b=de74 conjugacy classes — view the full character table.
| maximal subgroup of | #11718419, #11718422, #11718427, … |
| maximal normal subgroup of | #11718419, #11718422, #11718427, … |
| maximal quotient of | #11718072, #11718079, #11718086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 15);