Finite Group DatabasebetaFinite Group Databasebeta| order | 17488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#17983840 |
| unambiguous semidirect product | (C2×#17983840)⋊C2 |
| Fitting | C22×C1093 ⋊ C4 |
| Sylow | C1093 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4372 |
Polycyclic presentation:
2^4,1093|a^2=d,b^a=bc,e^a=e^563,e^d=e^10921102 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46854165, #46854166, C2×C22⋊#17983840, … |
| maximal normal subgroup of | #46854165, #46854166, C2×C22⋊#17983840, … |
| maximal quotient of | (C2×#17983840)⋊C4, C22⋊#22576727, #46854164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17488, 45);