Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | A4×D72 |
| Fitting, socle, derived | C22×C72 ⋊ C22×C3 |
| Hall | C22×D72 ⋊ C3 |
| Sylow | C72 ⋊ C22×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72 | C22×C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72215039, A4×#64423⋊C2, D72×S4 |
| maximal normal subgroup of | A4×#64423⋊C2, D72×S4 |
| maximal quotient of | #72215039 |
Past the SmallGroups library coverage — no SmallGroups id.