Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#13096694 |
| Fitting | C3×C72×D4 ⋊ C22 |
| Hall | C3×C72 ⋊ C2×#41 |
| Sylow | C72 ⋊ C2×C3×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D72 |
| commutator, cosocle | C2×C72 | C24×C3 |
| Frattini | C2 | C22×C3×D72 |
| Fitting | C3×C72×D4 | C22 |
| socle | C2×C3×C72 | C24 |
| hypercenter | C3×D4 | D72 |
| hypocenter | C72 | C2×C3×#41 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
818 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#13096694, C3×#72214319 |
| maximal normal subgroup of | D3×#13096694, C3×#72214319 |
Past the SmallGroups library coverage — no SmallGroups id.