Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #117 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(19,23)(22,25);(18,20,21,24)(19,22,23,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17)(18,19)(20,22)(21,23)(24,25)Polycyclic presentation:
2^5,13|a^2=d,b^2=e,c^a=ce,f^a=f^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #11718115, #11718123, #11718147, … |
| maximal normal subgroup of | #11718115, #11718123, #11718147, … |
| maximal quotient of | #11718586, #11718587, #11718593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 147);