Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25×C32 |
| direct product | C22×#72213251 |
| Fitting | C26×C32 ⋊ C3⋊D3 |
| derived | (C22⋊A4)⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊(A4⋊S4) |
| commutator, cosocle, hypocenter | (C22⋊A4)⋊H(3,𝔽3) | C23 |
| Frattini | C3 | C22×C3⋊(A4⋊S4) |
| Fitting | C26×C32 | C3⋊D3 |
| socle | C26×C3 | C3⋊(C3⋊D3) |
| LCS | G ▷ (C22⋊A4)⋊H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
9443 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 9443 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
200 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.