Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #102 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(19,22)(20,25)(23,24);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17)(18,19)(20,22)(21,24)(23,25)Polycyclic presentation:
2^5,13|a^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^12,d^b=de74 conjugacy classes — view the full character table.
| maximal subgroup of | #11718420, #11718421, #11718422, … |
| maximal normal subgroup of | #11718420, #11718421, #11718422, … |
| maximal quotient of | #11718121, D4⋊#1055, #11718129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 39);