Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #470 |
110 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,14,16,21)(13,17,19,26)(15,24,25,22)(18,27,23,20);(8,9)(10,11)(14,21)(17,26)(20,27)(22,24);(2,3)(4,5)(6,7)(9,11)(12,13,16,19)(14,20,21,27)(15,23,25,18)(17,24,26,22)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=cef,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11737602, #11737607, #11737609, … |
| maximal normal subgroup of | #11737602, #11737607, #11737609, … |
| maximal quotient of | #11727267, #11727270, #11727272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 586);