Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C541 ⋊ C2 |
| Sylow | C541 ⋊ #135 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^540,d^b=de,f^b=f^5404334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46829981, #46829983, #46829984, … |
| maximal normal subgroup of | #46829981, #46829983, #46829984, … |
| maximal quotient of | #46830172, #46830213, C4×D4328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 168);