Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#2199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C59 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C59 ◁ C2×D4×C59 ◁ G | |
270 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1003 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 931);