Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C7 |
| direct product | D3×C4⋊(C7⋊D7) |
| Fitting | C3×C4×C72 ⋊ C22 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ D3×D4 |
| Sylow | C3 ⋊ C2×C4⋊(C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×C7⋊D7 |
| commutator, socle, cosocle | C2×C3×C72 | C23 |
| Fitting | C3×C4×C72 | C22 |
| hypercenter | C4 | D3×C7⋊D7 |
| hypocenter | C3×C72 | C2×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 ◁ C4 | |
540 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 588 |
303 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D4×C7⋊D7, C2×D3×C4⋊(C7⋊D7), D3×C4⋊#64424, … |
| maximal normal subgroup of | D3×D4×C7⋊D7, C2×D3×C4⋊(C7⋊D7), D3×C4⋊#64424, … |
| maximal quotient of | C2×D3×C4⋊(C7⋊D7) |
Past the SmallGroups library coverage — no SmallGroups id.