Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#41×D59 |
| Fitting | C4×#41×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C4×#41×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C4×#41 | D59 |
| hypocenter | C59 | C2×C4×#41 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C4×#41 | |
1728 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1476, D59×#1477, #28555060, … |
| maximal normal subgroup of | D59×#1476, D59×#1477, #28555060, … |
| maximal quotient of | C4×#117×D59, C42×D4×D59, C42×Q8×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17687);