Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D472 |
| Fitting | C23×C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D236 |
| commutator | C4×C59 | C25 |
| Frattini | C4 | C24×D59 |
| Fitting | C23×C8×C59 | C2 |
| socle | C24×C59 | D4 |
| hypercenter | C23×C8 | D59 |
| hypocenter | C59 | C23×D8 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28495487, #28495489, #28495513, … |
| maximal normal subgroup of | #28495487, #28495489, #28495513, … |
| maximal quotient of | C23×#14273649, C23×#14273661, C22×C4×D472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19226);