Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6095 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #103 |
42 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)(14,16,17,15)(18,19,20,22,21,23,24,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,17,16)(19,22)(20,24)(23,25)Polycyclic presentation:
2^5,13|a^2=d,b^2=cd,c^2=e,b^a=bc,c^a=ce,f^a=f^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #11718342, C4×#6095, #11718358, … |
| maximal normal subgroup of | #11718342, C4×#6095, #11718358, … |
| maximal quotient of | #11718048, #11718059, #11718073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 23);