Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#14524194 |
| unambiguous semidirect product | D541⋊(C4⋊C4) |
| Fitting | C2×C4×C541 ⋊ C4 |
| Sylow | C541 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831048, #46831049, #46831054, … |
| maximal normal subgroup of | #46831048, #46831049, #46831054, … |
| maximal quotient of | C2×(C2×#14524194)⋊C4, C4×C4⋊#14524194, #46831117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 224);