Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89308 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #365 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,13,11,15,16,20,12,14,17,19,18,21,23,22);(2,3)(4,5)(6,7)(9,13,14,19)(10,16)(11,18)(15,22,21,20)(17,23)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,c^b=cf76 conjugacy classes — view the full character table.
| maximal subgroup of | #11726844, #11726845, #11726870, … |
| maximal normal subgroup of | #11726844, #11726845, #11726870, … |
| maximal quotient of | #11725319, #11725622, C2×#89308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 70);