Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic1082 |
| Sylow | C541 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
4340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46829905, #46829907, C4×#22575824, … |
| maximal normal subgroup of | #46829905, #46829907, C4×#22575824, … |
| maximal quotient of | C4×C4⋊Dic541, C4×#22575815, #46830058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 112);