Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#1159 |
| Fitting | C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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 — 4 generators on 19 points:
(1,2,4,6,7,5,3)(13,17)(14,18);(12,14,15,18)(13,16,17,19);(2,3)(4,5)(6,7)(12,13)(14,16)(15,17)(18,19);(8,9,10,11)100 conjugacy classes — view the full character table.
| maximal subgroup of | #11725919, #11725920, #11725927, … |
| maximal normal subgroup of | #11725919, #11725920, #11725927, … |
| maximal quotient of | C4×#6440, C4×(C22⋊D7)⋊C4, C4×#6449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 989);