Finite Group DatabasebetaFinite Group Databasebeta| order | 5888 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #13742 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#13743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | C2×D32 |
| commutator, Frattini, cosocle | C32 | C23×C23 |
| prime radical | C23×#2262 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ C2×C16×C23 ◁ C2×C23×C32 ◁ G | |
126 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5888, 6731);