Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#14524194 |
| unambiguous semidirect product | D541⋊C42 |
| Fitting | C2×C4×C541 ⋊ C4 |
| derived, Sylow | C541 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×#14524194)⋊C8, #46831045, #46831047, … |
| maximal normal subgroup of | (C2×#14524194)⋊C8, #46831045, #46831047, … |
| maximal quotient of | C42×#14524194, C2×(C2×#14524194)⋊C4, #46831111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 222);