Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#87639 |
| derived, Sylow | C72 ⋊ C22×C3×C4 |
| Hall | C3×C72 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D72 |
| commutator, hypocenter | C72 | C22×C3×C4 |
| Frattini | C2 | C2×C3×D72 |
| Fitting, socle | C22×C3×C72 | C22 |
| prime radical | C22×C3×C7⋊D7 | C2 |
| cosocle | C2×C72 | C23×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C3 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×#87639, C2×C3×#11716115, C2×#72222113, … |
| maximal normal subgroup of | C2×D3×#87639, C2×C3×#11716115, C2×#72222113, … |
| maximal quotient of | C3×#13096284 |
Past the SmallGroups library coverage — no SmallGroups id.