Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C9 |
| direct product | C22×#10619673 |
| Fitting | C24×C92 ⋊ C2 |
| Sylow | C92 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×C9⋊D9 |
| commutator, cosocle | C2×C92 | C24 |
| Frattini | C2×C32 | C23×C3⋊D3 |
| Fitting | C24×C92 | C2 |
| socle | C23×C32 | C2×C3⋊D3 |
| hypercenter | C24 | C9⋊D9 |
| hypocenter | C92 | C22×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C23 ◁ C24 | |
2714 conjugacy classes of subgroups; only the 672 normal subgroups are shown.
This group has 2714 conjugacy classes of subgroups — too many to draw. Only its 672 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1296 |
660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D4×C9⋊D9, C22×#14517678 |
| maximal normal subgroup of | C22×D4×C9⋊D9, C22×#14517678 |
| maximal quotient of | C2×#72244713, C2×#72252666 |
Past the SmallGroups library coverage — no SmallGroups id.