Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14524194)⋊C4 |
| Fitting | C2×C4×C541 ⋊ C4 |
| Sylow | C541 ⋊ #95 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=d,b^2=e,b^a=bc,f^a=f^52,f^d=f^5401100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831026, #46831027, #46831028, … |
| maximal normal subgroup of | #46831026, #46831027, #46831028, … |
| maximal quotient of | (C2×#14524194)⋊C8, #46831041, #46831042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 197);