Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic118 |
| Sylow | C59 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C4×M16×C59 | C2 |
| hypercenter | C4×M16 | D59 |
| hypocenter | C59 | Q8×M16 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
388 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28483023, #28483027, #28483037, … |
| maximal normal subgroup of | #28483023, #28483027, #28483037, … |
| maximal quotient of | M16×C4⋊Dic59, M16×Dic59⋊C4, #28587338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13463);