Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D2164 |
| Fitting | C22×C4×C541 ⋊ C2 |
| Sylow | C541 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D541 |
| commutator, cosocle | C2×C541 | C24 |
| Frattini | C2 | C23×D541 |
| Fitting | C22×C4×C541 | C2 |
| socle | C23×C541 | C22 |
| hypercenter | C22×C4 | D541 |
| hypocenter | C541 | C22×D4 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
4340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830053, #46830076, #46830077, … |
| maximal normal subgroup of | #46830053, #46830076, #46830077, … |
| maximal quotient of | C22×#22575813, C22×C4⋊Dic541, C2×C4×D2164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 184);