Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#14524194 |
| Fitting | D4×C541 ⋊ C4 |
| Sylow | C541 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2164 |
695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×#14524194, SD16×#14524194, #46831214, … |
| maximal normal subgroup of | D8×#14524194, SD16×#14524194, #46831214, … |
| maximal quotient of | C22⋊C4×#14524194, C4⋊C4×#14524194, #46831122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 226);