Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#1409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #353 |
| commutator | C42 | C2×C4×C59 |
| Frattini, cosocle | #127 | C22×C59 |
| prime radical | #127×C59 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C59 ◁ C2×C4×C59 ◁ #127×C59 ◁ G | |
110 conjugacy classes of subgroups.
1003 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 141);