Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #456 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,13,9)(10,17,18,14)(12,15,22,20)(16,21,23,19);(8,10)(9,14)(11,17)(12,21)(13,18)(15,23)(16,20)(19,22);(2,3)(4,5)(6,7)(8,9,13,11)(10,16,18,23)(12,20,22,15)(14,21,17,19)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,d^b=df,e^b=ef,e^c=ef67 conjugacy classes — view the full character table.
| maximal subgroup of | #11728742, #11728743, #11728747, … |
| maximal normal subgroup of | #11728742, #11728743, #11728747, … |
| maximal quotient of | #11729412, #11729414, #11729418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 780);