Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C541 ⋊ C2 |
| Sylow | C541 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D541 |
| commutator, cosocle | C4×C541 | C23 |
| Frattini | C4 | C22×D541 |
| Fitting | Q16×C541 | C2 |
| socle | C2×C541 | C2×D4 |
| hypercenter | Q16 | D541 |
| hypocenter | C541 | #135 |
| LCS | G ▷ C4×C541 ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
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^540,f^c=f^5401904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830606, #46830608, #46830612, … |
| maximal normal subgroup of | #46830606, #46830608, #46830612, … |
| maximal quotient of | #46830170, #46830212, #46830257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 169);