Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C92 · Schur multiplier (H2) = C24×C9 |
| direct product | C92×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C92 | C23 |
| commutator | C22 | C23×C92 |
| Frattini, socle, cosocle | C22×C32 | C23×C32 |
| prime radical | C32×#120 | C32 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C92 ◁ G | |
1495 conjugacy classes of subgroups; only the 598 normal subgroups are shown.
This group has 1495 conjugacy classes of subgroups — too many to draw. Only its 598 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #120×#6900, #120×C9⋊D9, C9×#10588712 |
| maximal normal subgroup of | #120×#6900, #120×C9⋊D9, C9×#10588712 |
Past the SmallGroups library coverage — no SmallGroups id.