Finite Group DatabasebetaFinite Group Databasebeta| order | 7659 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#66524 |
| derived, Sylow | C37 ⋊ C9×C23 |
| Hall | C23×C37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C37⋊C3 |
| commutator, hypocenter | C37 | C9×C23 |
| Frattini | C3 | C23×C37⋊C3 |
| Fitting, socle | C3×C23×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C23 | |
12 conjugacy classes of subgroups.
1035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×#66524, C23×#66524⋊C2, D23×#66524, … |
| maximal normal subgroup of | C2×C23×#66524, C23×#66524⋊C2, D23×#66524, … |
| maximal quotient of | C2×C23×#66524, C23×C22⋊#66524, C5×C23×#66524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7659, 2);