Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#11924175 |
| Hall | C2×#87640 ⋊ C3 |
| Hall | #3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #64423⋊C2 |
| commutator, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C2×#64423⋊C2 |
| Fitting, socle | C22×C72 | C22×C3 |
| hypocenter | C72 | C2×C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214112, C2×#72214099, C2×#72214061, … |
| maximal normal subgroup of | C2×#72214112, C2×#72214099, C2×#72214061, … |
Past the SmallGroups library coverage — no SmallGroups id.