Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#13051 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C23 |
| Frattini, cosocle | C2×#41 | C23×C23 |
| socle | C2×C23 | #1889 |
| prime radical | C23×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
632 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 6039);