Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | D3×#15123 |
| Fitting | C3×#15123 ⋊ C2 |
| Sylow | C3 ⋊ C2×#15123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C24×D3 |
| commutator, socle, cosocle | C24×C3 | C25 |
| Fitting | C3×#15123 | C2 |
| hypercenter | #15123 | D3 |
| hypocenter | C3 | C2×#15123 |
| LCS | G ▷ C24×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ #15123 | |
26444 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#616967, D3×#4306523, D3×#772785 |
| maximal normal subgroup of | D3×#616967, D3×#4306523, D3×#772785 |
Past the SmallGroups library coverage — no SmallGroups id.