Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | S4×GL(2,ℤ/4) |
| Fitting | C26 ⋊ D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×S42 |
| commutator, cosocle | C2×A42 | C23 |
| Fitting | C26 | D32 |
| socle | C25 | C2×D32 |
| hypercenter | C22 | S42 |
| hypocenter | A42 | C2×D4 |
| LCS | G ▷ C2×A42 ▷ A42 | |
| UCS | C1 ◁ C2 ◁ C22 | |
3145 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 3145 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
70 conjugacy classes — view the full character table.
| maximal subgroup of | S4×A4⋊S4, D4×S42, #72259050, … |
| maximal normal subgroup of | D4×S42, #72259050, #72259102 |
| maximal quotient of | GL(2,𝔽3)×GL(2,ℤ/4) |
| automorphism group of | C42×A4 |
Past the SmallGroups library coverage — no SmallGroups id.