Finite Group DatabasebetaFinite Group Databasebeta| order | 7268 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C79 · Schur multiplier (H2) = C2 |
| direct product | C2×D23×C79 |
| unambiguous semidirect product | C23⋊(C22×C79) |
| unambiguous semidirect product | (C2×C23)⋊(C2×C79) |
| Fitting, socle | C2×C23×C79 ⋊ C2 |
| derived, Sylow | C23 ⋊ C22×C79 |
| Hall | C23×C79 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | D23 |
| commutator, hypocenter | C23 | C22×C79 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C79 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C79 | |
20 conjugacy classes of subgroups.
2054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D23×C79⋊C3, D3×D23×C79, C2×C3×D23×C79, … |
| maximal normal subgroup of | C2×D23×C79⋊C3, C2×C3×D23×C79, C2×C5×D23×C79 |
| maximal quotient of | D3×D23×C79, C2×C3×D23×C79, C2×C79×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7268, 8);