Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×D92 |
| Fitting | C2×D4×C92 ⋊ C22 |
| Sylow | C92 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D92 |
| commutator, cosocle | C2×C92 | C25 |
| Frattini | C2×C32 | C23×D32 |
| Fitting | C2×D4×C92 | C22 |
| socle | C22×C32 | C22×D32 |
| hypercenter | C2×D4 | D92 |
| hypocenter | C92 | C23×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
6955 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.