Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C3⋊D3×#3484 |
| Fitting | C32×#3484 ⋊ C2 |
| Sylow | C32 ⋊ C2×#3484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C26 |
| Fitting | C32×#3484 | C2 |
| hypercenter | #3484 | C3⋊D3 |
| hypocenter | C32 | C2×#3484 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #3484 | |
43314 conjugacy classes of subgroups.
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72252304, #72252356 |
| maximal normal subgroup of | #72214863, #72252304, #72252356 |
Past the SmallGroups library coverage — no SmallGroups id.