Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×Dic271 |
| Sylow | C271 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
2740 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×Dic271, #103×Dic271, #46836196, … |
| maximal normal subgroup of | #101×Dic271, #103×Dic271, #46836196, … |
| maximal quotient of | C2×C4⋊C4×Dic271, C4×Q8×Dic271, C2×#31773783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 1015);