Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C541 ⋊ C4 |
| Sylow | C541 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|a^2=e,c^2=d,b^a=bd,f^a=f^52,f^e=f^5401100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46831042, #46831043, #46831046, … |
| maximal normal subgroup of | #46831042, #46831043, #46831046, … |
| maximal quotient of | #46831111, C4×C22⋊#14524194, C4×C4⋊#14524194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 225);