Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #473 |
100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(8,11,14,28)(9,16,19,34)(10,21,23,37)(12,27,13,26)(15,30,31,39)(17,33,18,24)(20,36,35,32)(22,38,29,25);(8,10)(9,15)(11,25)(12,22)(13,29)(14,23)(16,32)(17,20)(18,35)(19,31)(21,27)(24,39)(26,37)(28,38)(30,33)(34,36);(2,3)(4,5)(6,7)(8,9,14,19)(10,20,23,35)(11,24,28,33)(12,18,13,17)(15,29,31,22)(16,27,34,26)(21,30,37,39)(25,36,38,32)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,d^2=f,e^2=f,b^a=be,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,e^b=ef,d^c=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11737740, #11737741, #11737746, … |
| maximal normal subgroup of | #11737740, #11737741, #11737746, … |
| maximal quotient of | #11728054, #11728055, #11728058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 738);