Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#6399 |
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 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) = 17 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 17 points:
(3,4,6,8,9,7,5)(10,12,13,16,14,15,17,11);(4,5)(6,7)(8,9)(10,11)(12,13)(14,16)(15,17);(1,2)88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726468, #11726473, #11726482, … |
| maximal normal subgroup of | #11726468, #11726473, #11726482, … |
| maximal quotient of | C2×#89259, #11727551, C2×#89260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 672);