Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#10622085 |
| Fitting | C2×C11×C32 ⋊ C2 |
| Sylow | C11 ⋊ C2×M64 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14641583, C4×#10622085, #14673949, … |
| maximal normal subgroup of | #14641583, C4×#10622085, #14673949, … |
| maximal quotient of | C2×#13066749, C4×#10622085, C2×(C2×D11)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6801);