Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C541 ⋊ C2 |
| Sylow | C541 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D541 |
| commutator, socle, cosocle | C22×C541 | C23 |
| Fitting | C42×C541 | C2 |
| prime radical | C2×D2164 | C2 |
| hypercenter | C42 | D541 |
| hypocenter | C541 | #124 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ C42 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^5404334 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46829914, #46830349, #46830354, … |
| maximal normal subgroup of | #46829914, #46830349, #46830354, … |
| maximal quotient of | #46830041, #46830066, #46830077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 134);