Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D239 |
| Fitting | D8×C239 ⋊ C2 |
| Sylow | C239 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D239 |
| commutator | C4×C239 | C23 |
| Frattini | C4 | C22×D239 |
| Fitting | D8×C239 | C2 |
| socle | C2×C239 | C2×D4 |
| hypercenter | D8 | D239 |
| hypocenter | C239 | C2×D8 |
| LCS | G ▷ C4×C239 ▷ C2×C239 ▷ C239 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
76 conjugacy classes of subgroups.
847 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D239, SD32×D239, #29505206, … |
| maximal normal subgroup of | D16×D239, SD32×D239, #29505206, … |
| maximal quotient of | #102×D239, #107×D239, #29504852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 155);