Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C541 ⋊ C4 |
| Sylow | C541 ⋊ #107 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=d,b^2=ce,c^2=e,b^a=bc,c^a=ce,f^a=f^52,f^d=f^5401094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831087, #46831088, #46831101, … |
| maximal normal subgroup of | #46831087, #46831088, #46831101, … |
| maximal quotient of | #46831038, #46831039, #46831049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 215);