Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#1325 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #99 |
| commutator | C2×C4 | C2×C8×C59 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C59 |
| prime radical | C23×C59 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C59 ◁ C2×C4⋊C4×C59 ◁ G | |
134 conjugacy classes of subgroups.
1534 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 57);