Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#11924212 |
| Fitting | C23×C72 ⋊ C2×C3 |
| Hall | C2×C7×C22⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#64422 |
| commutator, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C22×#64422 |
| Fitting | C23×C72 | C2×C3 |
| socle | C22×C72 | C22×C3 |
| hypercenter | C23 | #64422 |
| hypocenter | C72 | C2×C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ C23 | |
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222022, C2×ΓL(1,𝔽8)×(C22⋊D7)⋊C3, #72246007, … |
| maximal normal subgroup of | C2×#72222022, C2×ΓL(1,𝔽8)×(C22⋊D7)⋊C3, #72246007, … |
| maximal quotient of | #72245106, #72246048, #72246132 |
Past the SmallGroups library coverage — no SmallGroups id.