Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#1792 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #120 |
| commutator | C2×C4 | C22×C4×C59 |
| Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C2×H(5,𝔽2)×C59 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
620 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 524);