Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×(C2×D7)⋊C8 |
| Fitting | C22×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 21 points:
(4,6)(7,8,10,12,13,11,9)(14,15,16,18,17,19,20,21);(3,4)(5,6)(8,9)(10,11)(12,13);(1,2)136 conjugacy classes — view the full character table.
| maximal subgroup of | #11725328, #11726353, #11726354, … |
| maximal normal subgroup of | #11725328, #11726353, #11726354, … |
| maximal quotient of | C2×#89254, #11727488, C2×#89251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 642);