Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ C4⋊C8 |
38 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)(15,17)(18,19,20,22,21,23,24,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17)Polycyclic presentation:
2^5,13|a^2=d,b^2=c,c^2=e,b^a=bd,f^a=f^12116 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic26, #11718340, #11718346, … |
| maximal normal subgroup of | C8×Dic26, #11718340, #11718346, … |
| maximal quotient of | #11718071, #11718072, #11718093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 21);