Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#67003 |
| Fitting | C4×C11×#41 ⋊ C2 |
| Sylow | C11 ⋊ C4×#135 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14723147, C8×#67003, #14723175, … |
| maximal normal subgroup of | #14723147, C8×#67003, #14723175, … |
| maximal quotient of | C8×#67003, #14723300, #14723304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13280);