Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23900 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C28×C3 |
| direct product | C32×#23900 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C32 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C25×C32 ◁ G | |
10560 conjugacy classes of subgroups.
414 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C3×#72231563 |
| maximal subgroup of | C3×#72231563 |
| maximal normal subgroup of | C3×#72231563 |
Past the SmallGroups library coverage — no SmallGroups id.