Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D541 |
| Fitting | D8×C541 ⋊ C2 |
| Sylow | C541 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D541 |
| commutator, cosocle | C4×C541 | C23 |
| Frattini | C4 | C22×D541 |
| Fitting | D8×C541 | C2 |
| socle | C2×C541 | C2×D4 |
| hypercenter | D8 | D541 |
| hypocenter | C541 | C2×D8 |
| LCS | G ▷ C4×C541 ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
1904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D16×D541, SD32×D541, #46830609, … |
| maximal normal subgroup of | D16×D541, SD32×D541, #46830609, … |
| maximal quotient of | #102×D541, #107×D541, #46830255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 155);