Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D541⋊C16 |
| derived, Sylow | C541 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14524194 |
| commutator, hypocenter | C541 | C2×C16 |
| Frattini | C4 | C2×#14524194 |
| Fitting | C8×C541 | C4 |
| socle | C2×C541 | C2×C8 |
| prime radical | C2×D541 | C8 |
| cosocle | #16864513 | C22 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|a^2=c,c^2=d,d^2=e,f^a=f^52,f^b=f^540,f^c=f^5401112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14524194, #46831062, #46831087, … |
| maximal normal subgroup of | C16×#14524194, #46831062, #46831087, … |
| maximal quotient of | #46831061, #46831070, #46831096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 219);