Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #440 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,10,11,9)(12,13)(14,19)(15,16)(17,18);(13,17)(14,18)(16,19);(2,3)(4,5)(6,7)(8,9,11,10)(13,16)(17,19)Polycyclic presentation:
2^6,7|a^2=e,c^2=e,d^2=f,c^a=cf,g^a=g^6,c^b=cd,d^b=df,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89529, #11736171, #11736207, … |
| maximal normal subgroup of | C2×#89529, #11736171, #11736207, … |
| maximal quotient of | #11725904, #11725910, #11725913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 291);