Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C212 |
| direct product | C3×#72219157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #35346 |
| commutator, Frattini, cosocle | C25 | C25×C3 |
| LCS | G ▷ C25 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C25×C3 ◁ G | |
At least 6512 conjugacy classes of subgroups; only the 2018 normal subgroups are shown.
336 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | #72270313, D3×#72219157 |
| maximal subgroup of | #72270313, D3×#72219157, C3×#72219167 |
| maximal normal subgroup of | #72270313, D3×#72219157, C3×#72219167 |
Past the SmallGroups library coverage — no SmallGroups id.