Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #41×D236 |
| Fitting | C4×#41×C59 ⋊ C2 |
| Sylow | C59 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C4×#41×C59 | C2 |
| hypercenter | C4×#41 | D59 |
| hypocenter | C59 | D4×#41 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1648 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28480710, #28480714, #28555546, … |
| maximal normal subgroup of | #28480710, #28480714, #28555546, … |
| maximal quotient of | #41×(C2×D59)⋊C4, #41×C4⋊Dic59, #117×D236, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18001);