Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6505 |
| Fitting | C22×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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:
(3,4,6,8,9,7,5)(10,13,14,23)(11,16,18,25)(12,19,20,22)(15,21,17,24);(1,2)(10,12,14,20)(11,15,18,17)(13,22,23,19)(16,24,25,21);(4,5)(6,7)(8,9)(10,11)(12,15)(13,21)(14,18)(16,22)(17,20)(19,25)(23,24);(1,2)82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727447, #11727448, #11727864, … |
| maximal normal subgroup of | #11727447, #11727448, #11727864, … |
| maximal quotient of | C2×#89736, C2×#89738, C2×#89739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1261);