Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D541 |
| commutator, socle | C2×C541 | C22×C4 |
| Fitting | M16×C541 | C2 |
| prime radical | #22575836 | C2 |
| cosocle | C4×C541 | C23 |
| hypercenter | M16 | D541 |
| hypocenter | C541 | #131 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|a^2=d,d^2=e,f^a=f^540,c^b=ce,f^c=f^5402720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830289, #46830291, #46830294, … |
| maximal normal subgroup of | #46830289, #46830291, #46830294, … |
| maximal quotient of | #46830132, #46830133, #46830140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 154);