Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C7 |
| direct product | C2×#11924241 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×C4⋊(C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×C7⋊D7 |
| commutator, cosocle | C2×C3×C72 | C23 |
| Frattini | C2 | C2×D3×C7⋊D7 |
| Fitting, socle | C22×C3×C72 | C22 |
| hypocenter | C3×C72 | C2×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1176 |
306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×C4⋊(C7⋊D7), C2×#67×C7⋊D7, C2×#72245569, … |
| maximal normal subgroup of | C2×D3×C4⋊(C7⋊D7), C2×#67×C7⋊D7, C2×#72245569, … |
Past the SmallGroups library coverage — no SmallGroups id.