Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic239 |
| derived, Sylow | C239 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D239 |
| commutator, hypocenter | C239 | C23×C4 |
| Frattini | C2 | C23×D239 |
| Fitting, socle | C24×C239 | C2 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C239⋊#95, C22⋊C4×Dic239, #29504630, … |
| maximal normal subgroup of | C2×C239⋊#95, C22⋊C4×Dic239, #29504630, … |
| maximal quotient of | C22×C4×Dic239, C22×C22⋊Dic239, C22×C4⋊Dic239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 181);