Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#63579 |
| Sylow | C33 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | D32 |
| commutator | C2×C32 | C2×C3×C42 |
| Frattini | C23 | C2×C3×D32 |
| Fitting, socle, prime radical | C24×C33 | C22 |
| cosocle | C23×C32 | C23×C3 |
| hypocenter | C32 | C2×C3×#95 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C24×C3 | |
2162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24771);