Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#6487 |
| Sylow | C7 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 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 — 4 generators on 21 points:
(3,4)(5,6)(7,8,10,12,13,11,9);(1,2)(14,16,17,21)(15,18,19,20);(4,6)(8,9)(10,11)(12,13)(14,15,17,19)(16,20,21,18);(1,2)124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89247, #11727199, #11727211, … |
| maximal normal subgroup of | C2×#89247, #11727199, #11727211, … |
| maximal quotient of | C2×#89705, C2×#89700, C2×#89701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1237);