Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#16837235 |
| Fitting | C2×C32×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16 | C2×D59 |
| commutator | C2×C59 | C22×C16 |
| Frattini | C16 | C22×D59 |
| Fitting | C2×C32×C59 | C2 |
| socle | C22×C59 | C2×C16 |
| hypercenter | C2×C32 | D59 |
| hypocenter | C59 | C2×M64 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C16 ◁ C2×C32 | |
112 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476499, C4×#16837235, #28508865, … |
| maximal normal subgroup of | #28476499, C4×#16837235, #28508865, … |
| maximal quotient of | C2×#21422229, C4×#16837235, C2×(C2×D59)⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6801);