Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D541 |
| unambiguous semidirect product | C541⋊C25 |
| unambiguous semidirect product | (C2×C541)⋊C24 |
| Fitting, socle | C24×C541 ⋊ C2 |
| derived, Sylow | C541 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D541 |
| commutator, cosocle, hypocenter | C541 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C541 | C2 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
4352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830030, C2×C22⋊C4×D541, C22×#22575813, … |
| maximal normal subgroup of | #46830030, C2×C22⋊C4×D541, C22×#22575813, … |
| maximal quotient of | C23×C4×D541, C24×Dic541, C22×D4×D541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 195);