Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| 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)(14,15,16,17)(20,24)(22,25);(18,20)(19,22)(21,24)(23,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(18,19,21,23)(20,22,24,25)Polycyclic presentation:
2^5,13|a^2=e,c^2=d,f^a=f^12,c^b=ce80 conjugacy classes — view the full character table.
| maximal subgroup of | #11718239, #11718401, #11719062, … |
| maximal normal subgroup of | #11718239, #11718401, #11719062, … |
| maximal quotient of | #11718309, #11718310, #11718311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 98);