Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C541 ⋊ C2 |
| Sylow | C541 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D541 |
| commutator, socle, cosocle | C22×C541 | C23 |
| Fitting | C4⋊C4×C541 | C2 |
| prime radical | C2×D2164 | C2 |
| hypercenter | C4⋊C4 | D541 |
| hypocenter | C541 | #123 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^5,541|c^2=d,b^a=bd,c^a=ce,f^a=f^540,f^b=f^5402714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D541, C2×#31772613, #46830684, … |
| maximal normal subgroup of | #123×D541, C2×#31772613, #46830684, … |
| maximal quotient of | #46830037, #46830046, #46830053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 131);