Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #455 |
152 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)(11,21)(14,19)(16,23)(18,20);(8,10)(9,13)(11,20)(12,17)(14,23)(15,22)(16,19)(18,21);(2,3)(4,5)(6,7)(8,9,12,15)(10,16,17,23)(11,19,21,14)(13,20,22,18)Polycyclic presentation:
2^6,7|a^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 | #11728751, #11728752, #11728754, … |
| maximal normal subgroup of | #11728751, #11728752, #11728754, … |
| maximal quotient of | #11729401, #11729403, #11729419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 776);