Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#41×D59 |
| Fitting | C22×#41×C59 ⋊ C2 |
| Sylow | C59 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C22×#41×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C22×#41 | D59 |
| hypocenter | C59 | C23×#41 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
6520 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1780, #28587800, #28587804, … |
| maximal normal subgroup of | D59×#1780, #28587800, #28587804, … |
| maximal quotient of | C22×#117×D59, C22×C4×D4×D59, C22×C4×Q8×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19306);