Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C25 |
| direct product | S4×#1020 |
| Fitting, socle | C26 ⋊ D32 |
| derived | A4×C22⋊A4 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | A4×C22⋊A4 | C22 |
| Fitting, socle | C26 | D32 |
| LCS | G ▷ A4×C22⋊A4 | |
| UCS | C1 | |
2789 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 2789 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
50 conjugacy classes — view the full character table.
| maximal subgroup of | S4×A4⋊S4, #10202, S4×#1020⋊C2, … |
| maximal normal subgroup of | S4×#1020⋊C2 |
| maximal quotient of | #10202, GL(2,𝔽3)×#1020, S4×#5934, … |
| automorphism group of | Q8×SL(2,𝔽3) |
Past the SmallGroups library coverage — no SmallGroups id.