Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D7 |
| Fitting | C22×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 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)(9,11);(2,3)(4,5)(6,7)(8,9)(10,11);(12,13,14,16,15,17,18,19)136 conjugacy classes — view the full character table.
| maximal subgroup of | (C22⋊D7)⋊C16, #11726856, #11726857, … |
| maximal normal subgroup of | (C22⋊D7)⋊C16, #11726856, #11726857, … |
| maximal quotient of | C8×(C2×D7)⋊C4, C8×Dic7⋊C4, #11727538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 643);