Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #568×D59 |
| Fitting | C59×#568 ⋊ C2 |
| Sylow | C59 ⋊ C2×#568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D59 |
| commutator, socle | C2×C59 | C24×C4 |
| Fitting | C59×#568 | C2 |
| hypercenter | #568 | D59 |
| hypocenter | C59 | C2×#568 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1460 conjugacy classes of subgroups.
1054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1858, #28589533, D59×#1861, … |
| maximal normal subgroup of | D59×#1858, #28589533, D59×#1861, … |
| maximal quotient of | D59×#2873, D59×#2875, #568×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19217);