Finite Group DatabasebetaFinite Group Databasebeta| order | 416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C13 ⋊ C2 |
| Sylow | C13 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,20)(16,17)(19,21);(14,16,18,17)(15,19,21,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,19)(17,20)(18,21)Polycyclic presentation:
2^5,13|b^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^12,c^b=ce,d^c=de71 conjugacy classes — view the full character table.
| maximal subgroup of | #11718409, #11718410, #11718723, … |
| maximal normal subgroup of | #11718409, #11718410, #11718723, … |
| maximal quotient of | #11718625, #11718627, #11718629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(416, 153);