Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#6461 |
| Fitting | C2×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#126 |
246 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,6,8,9,7,5)(10,12,13,16)(11,15,14,17)(19,23)(22,25);(11,14)(12,16)(18,20,21,24)(19,22,23,25);(4,5)(6,7)(8,9)(10,11)(12,15)(13,14)(16,17)(18,19)(20,22)(21,23)(24,25);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725883, C4×#6461, #11731074, … |
| maximal normal subgroup of | #11725883, C4×#6461, #11731074, … |
| maximal quotient of | C2×#89423, C2×#89426, C2×#89441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 965);