Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×C22⋊D7 |
| Fitting | C23×C4×C7 ⋊ C2 |
| Sylow | C7 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(4,6)(11,12,14,16,17,15,13);(3,4)(5,6)(12,13)(14,15)(16,17);(1,2)(7,8,9,10);(1,2)136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6380, #11727284, #11727670, … |
| maximal normal subgroup of | C4×#6380, #11727284, #11727670, … |
| maximal quotient of | C2×C4×(C2×D7)⋊C4, C2×C4×Dic7⋊C4, C42×C22⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1241);