Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of #4323 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×#4325 |
| Fitting | C23×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C23×SD16 |
1720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14660574, #14660578, #14660601, … |
| maximal normal subgroup of | #14660574, #14660578, #14660601, … |
| maximal quotient of | C23×#66873, C23×#66899, C23×#66872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19228);