Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(2,𝔽5) |
| Fitting, socle | C2×C52 ⋊ GL(2,𝔽5) |
| derived | #72209598 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(2,𝔽5) |
| commutator, hypocenter | #72209598 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | GL(2,𝔽5) |
| prime radical | C2×#72210652 | C2 |
| cosocle | #72210652 | C22 |
| LCS | G ▷ #72209598 | |
| UCS | C1 ◁ C2 | |
456 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
58 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.