Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C239⋊C8 |
| derived, Sylow | C239 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D239 |
| commutator, hypocenter | C239 | C4×C8 |
| Frattini | C2×C4 | C2×D239 |
| Fitting | C42×C239 | C2 |
| socle | C22×C239 | C2×C4 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C239⋊C8, #29504493, #29504494, … |
| maximal normal subgroup of | C8×C239⋊C8, #29504493, #29504494, … |
| maximal quotient of | C8×C239⋊C8, #29504493, #29504527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 55);